sounds like you've tried all the tricks. bottle jacks make great hydraulic presses so if you can support the base of the jack somehow you may be able to press the hitch out utilising the hole you have drilled, an extension may be needed. also, if you do manage to get a bottle jack in there, put it under decent load and then heat the tow bar, i've lost count the amount of times i've been pressing off bearing races that wouldn't budge until heat is applied and all of a sudden they ' crack ' free. goodluck! 

How did it get stuck in the first place. Don't these have a bit of give (space). Wonder if you/someone reversed back and hit something hard and it's jammed in tight.

Take it back to the tow ball people (sorry don't know their name). They might be able to solve a tight situation.

 I had the same thing with my Pajero when I bought it.

Tried everything but the blowtorch.

What worked for me and it's not necessarily a good idea but I attached a very short chain to the towball and to my Wife's Astra Towball and Dropped the clutch jolting it several times and it came out

The photo doesn't show the underside of the hitch, my new Dmax has a locking bolt underneath, just a thought!!

 try getting a sledgy and give a a good few blows downwards as its standing now.....freed mine up this way then just kept lubricating it and knoked it out the other way

Just a quick thought from a ex boily , if I had done all that you have , then my next move would be

to split ( with a 1mm fine cutting disc , that outer square tube , that the hitch sits in, from under neath.

Not all the way to start with, maybe just a inch or so , just a bit, up near that re-enforceing collar, then try wacking it ,

if it dont budge , then split another inch or so etc etc, when it does release , the couple or more inchs you have split

will be dead easy for you or someone to mig back-up , taking care not to allow the penetration to build up inside the outer tube.

( a scrap piece of ali or brass g clamped inside while you weld will prevent it too)

If your near east freo , I will gladly mig it up for you.( away tom aft and fri morn) cheers.

maybe reverse fit the towball whilst on car and smack from underside with small sledge or try solid chain round tree then whilst under tension also smack it around with sledge .. good luck . 

If its stuck in why do you want to take it out? If it was me after all that trouble I'd put the bolts back in and leave it

.If you bump your shins on it, the first time is an accident, the second is you forgot about the first time and the third time says you are a forgetful idiot.

You said "have heated it up with a blow torch and cooled down rapidily with water".. That's how you shrink metal. So Im assuming its the insert you were heating not the sleeve or body? If not you've got the idea right but around the wrong way.

If it was me Id be heating the outside or sleeve with an oxy and possibly spraying the inside with a freeze spray and laying into it with a sledge hammer while still hot/cold.
Overheating it is probably not ideal, but it will loosed the rust if your getting to those extremes, and belt the crap out of the sides too.

Then Id be going along the lines of quadfisher, or cutting it off altogether

or Carnarvonite and say fuck it, and leave it like it is...LOL

Good luck

Had the same thing happen on the cruiser,Hairyone is on the money,heat it up and belt crap out of it.

I know its not the best option at all but I have heard of people doing this.

put the heaviest rated shackle you can find through the towball hole. attach a heavily rated snatch strap.
find the biggest tree you can and wrap other end around the snatch strap!
make sure every one is clear and give it chooks.
a snatch strap will stretch and at the right time give it plenty of oomph to pull it out and providing you have a decent quality snatch strap it wont break but it will pull the hitch out throwing it directly back at the tree.
as I said its not the best thing to do but the only thing I can see happening is the hitch hitting the tree at mad speeds.

Rather than trying to push/pull it out, try knocking it from side to side. This will be a lot easier to do and will probably be a good way to break the lock. If possible knock it from side to side whilst it is being pulled outwards.

Putting it back on the car and having it under tension with a strap whilst knocking side to side would be the go.

That's how I'd try anyway

 Cheers guys for your input, as I want it out so my wife can get better access when taking the pram out. Nothing worse than hearing your wife winge about it once she busted her leg over it.

Just wondering if that is a "Homemade" drawbar, made of RHS that is not the same profile and the female part of the towbar. If the corners are a tighter radius, its been sledged on and has picked up.
My thoughts would be to secure the towbar some how, weld a rod 15mm to 20mm dia along the axis of the draw bar, find a sliding weight to slide down on the rod and then weld a stop on the end of the rod. That way you can thump it off.

what area you located ill have a go at it im a mobile welder

 Take it to a rigging mob with a test bed.  Secure towball hole with shackle to hydraulic ram, framework to trolley with soft slings to spread the load and apply pressure.  At least the forces are controlled and the operator will have a shield to protect themselves.  Might cost you a carton or some $$$ but I wouldnt think it would take more than a few minutes. Nobles in Kewdale have a huge test bed and a few smaller standing rigging frames similar to the earlier idea of a bearing press, but in reverse.

 Carefully cut the tongue out with oxy then buy another tongue...or....heat up till glowing use a impact puller to shock out...friend made one up...and got mine and another one out while both still hooked to 4wds. Don't snatch...chain won't do it if same as mine...needs lots of heat and sudden impact...hard work but it did the job for me....imagine a length of solid rod...one end a u shape attached with hole to fit tongue hole with pin...heavy pipe over rod (used to slide up and down for impact) end of rod blanked off to stop pipe coming off end....heat around outside of tongue sleeve...use impact tool like someone's just taken your pride n joy and then some more....alternatively leave as is and you load the car for the wife....get another wife....heaps of options....put a sign up to warn her of hazard....

 Added some other photos and looks pretty badly stuck on the internal shot, sarcasm0 sounds like best option. Thx for offer thesuperviser but looks l like some heavy artillery will be required. Thinking other option without cutting open would be a big diggers jackhammer to punch it out. Cheers guys.

With the amount of rust shown in the photo, I'd say its not going to come out without major surgery.

Once it starts to rust, it swells and grows into the outer casing making it near impossible to remove

Buy a new one from the wreckers?

heat and multiple blows with a sledgy was the only thing that moved mine. press didn't work but mine was pretty bad

With that amount of rust Carnarvonite is right its not going anywhere without opening it up or at the very least a lot of heat. Rust has a powerful grab. I would suggest cutting the receiver off and making another one and a new hitch to suit. It may be tough now (hitch strength)but as it rusts further over time do you want the risk of a heavy trailer coming off at 100kph? I reckon bite the bullet. Cheers.

Had the same problem a few months ago,
I managed to free it by hitting in-wards in with a sledge hammer. Then put some rope around a big tree and the tow ball, put it under tension and kept hitting the tongue with the sledge hammer and it came free. Also used a lot of CRC.

And a lot of the "proceedures" mentioned are going to make me or some other doc a lot of money!!!!!

I would go the way off leaving it, get a new wife that wont winge or wreckers for another one.

Agreed, if mine was that rusted I wouldn't bother with the chain and jolting method

Perhaps just strap a piece of pool noodle foam around it so the wife doesn't hurt herself

How often do you tow? Leave the whole lot off and when you need it bolt it back on. Its only like 4 bolts?

 Put it back on your car, leave pin out and tow boat to around the block! If your luck is anything like mine this will work 50m from your driveway! 

Sorry mate. On a serious note where are you located? I could take it to work and sorting out piece of piss?? 

 Got motivated and picked up a 12lb sledge hammer from bunnings thinking not letting this stupid thing stop me. Gave it the bejeezes with more heat and lubricant and finally came out. Took a while but happy I accomplished beating the bloody thing. Cheers guys for offer anyway.

persistence paid off. bet your glad its finally out.

had the same prob with a falcon wagon I had, stayed in all the time. probably still stuck in it at the wreckers after it got written off by a drunk driver. I gave up on trying to remove it