I think there are two issues - one being the finances - do you know how stable his finances are, is he likely to bring debts with him? So this would be a deal breaker if he is feckless with money, or likely to want you to pay the majority of the expense because you earn more. Have you considered what will happen to the house when he moves in? As in, will it be half his? That would only be fair if he was contributing to half, or would you conintue to be the sole owner, so would that mean that you would have to continue to pay all of the mortgage? Then he could still argue a contribution to the house if for instance, you paid the mortgage and he paid the other bills. Is the flat he is living in now rented or does he own it? There are an awful lot of difficult questions there - but ones that i feel, with the right partner and right attitudes on each side are not insurmountable - however, he sounds like he either doesn't like to part with his cash or is actually quite hard-up due his living circumstances and having to pay fo the kids too - so that would potentially change when he moves in so the money he pays for rent/mortgage would become available to the family. If he has other debts, i would be very wary.
As i said, the above is sortable - your feelings for the children? I don't know - as i said, i know i could never be a step-mum, because i have my own children. I could NEVER feel the same about someone elses child and i would be lying if i said i wouldnt be jealous and resentful, no matter how nice the children are. You already find them clingy (and have said that you understand this, but still find it irritating) and that your parenting is very different. This i suppose would be less of an issue if it wasnt a 50% arrangement, but it is - the only thing is that they are getting older and will be less clingy, but they will be teenagers soon. I predict a few bouts of "you're not my mum" etc. But they will be spending more and more time with friends and locked in bedrooms playing grunge music.
The thing is, i think he could well feel similarly about his own/your children - this is evidenced by him saying that he doesn't want his child to get the smaller bedroom, that they should go to private school etc. I assume that the boy's father will contribute to this? So he could well be harbouring similar resentments towards your children but hiding them well - i am sure your interactions with his children are pleasant and he probably thinks you are good with them (which iam sure you are) but you can see what i am getting at?
As i say, i am very cynical about mixed families, simply becaue I would struggle - saying that, my DP is my DD1's step-father and it worked out ok, but there is no mistaking it, he is a very good step-dad and always been good to DD1, but never a "dad" and he totally and utterly adores his DD (my DD2) DD1 has left home now - there was a big gap, but i think it could have been an issue if she were younger - not that he would have let it show, but really, at the end of the day - your feelings are your feelings.