I wouldn't have been introducing a man to my kids if he wasn't introducing his to me and mine.
If he was going to introduce you now, to me that's actually about the right timing. A couple of years.
But he's not.
He's flying off the handle, telling you its not happening, telling you to shut up about it, and engineering arguments.
So, for whatever reasons, he still - at this reasonable time period, doesn't want you introduced to his child. As others have said, that suggests he doesn't see this as long haul.
If he did, now would he a very reasonable time to introduce you.
He's happy to take advantage of your company, happy to take advantage of your time, happy to take advantage of your money/resources to pay for a bolthole caravan. If he could afford it on his own, I imagine he'd just have gotten it on his own.
No doubt also happy to have regular sex on a plate.
Yet apparently doesn't see this as long-term/settled.
If you were in the same page - and if you were presumably you'd not have introduced your kids to him - that would be ok but, like many women, you're not.
(Interesting that he never married his child's mother either).
He's getting far too much commitment and openness and resources and intimacy etc from you; for a man who's apparently not committed enough to introduce his child after a reasonable period of time.
He's also got a nasty, immature way of dealing with things.
And he seems to think you're under his thumb. You can just shut up about this subject. There's little fear of you walking away, apparently.
This isn't an equal relationship.
I wouldn't be investing in it further. He doesn't seem invested in it. It's maybe just convenient for him.