it would be unfair for you to then change your mind and demand that two small children sell their family home and move into a much smaller home
Well to be fair to the OP - her DP and his ex created the conditions for this to potentially happen when they split up.
It's only because he's made the bizarre decision to keep paying half the mortgage that the kids are able to stay in that house. If he wasn't in a position to, they would have to move out and downsize whether OP was in the picture or not.
Yes he has an asset quietly appreciating in the background that OP cannot benefit from. But that also means his third child with OP cannot benefit from it either, which is a bit shit IMO.
I think, in the spirit of 'all children should be treated equal', he should try and make sure that, as the parent of all the children involved, he should treat them equally. Not keep two in 'the big house' and one in a cramped rented flat.
TBH he shouldn't have even entertained having a third child with a new partner until he was able to do that.
OP also needs to take some responsibility for having four years to see how this situation was set up and then somehow be surprised that it's not changing just because she had a baby. The time for all these kinds of conversations was before getting pregnant.