“Buy the house yourselves, and transfer equity to the children on a schedule”
That would also probably be subject to gift tax.
Not if the scheduled transfers are less than the cap
“as they pay the mortgage/rent.”
And if they get fed up with your controlling behavior, they can stop paying the mortgage and YOU will get foreclosed upon.
Possibly. Or they try to sell.
I feel sorry for your daughter and future son-in-law.
I agree that it is a horrid idea, but the solution happens to fit all of the OP’s requirements. Personally, I say let them rent and earn the down payment on their own. They will appreciate their new home much more if they actually paid for it. As I said earlier:
If I were the children, I would run from such a scenario (as it makes them dependent on you), but then again, I would (hopefully) be able to afford my own down payment at some point.