aries, Im sure you are advising the above goodheartedly and with the best of seichel and intentions, but
1- Financially it doesnt make sense for us to give money thats irreplaceable and might end up in places we dont want it to. You, by comparison, B”H, seem to be somewhat of a bank, lending money left and right as the need arises to relatives and friends. We cant and we dont.
2- Nor does it make sense for the couple to continue paying rent and paying up their landlord’s mortgage.
So, Im asking for the most tactful way to accomplish the goals in the most sensitive and least painful manner and with the least financial risk and potential for regret.
Buy the house yourselves, and transfer equity to the children on a schedule as they pay the mortgage/rent. Just make sure you get a lawyer that can write up the document correctly, and probably a Heter Iska as well (speak to your Rov).
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.
Make sure to discuss with both of your children and get their input.
Good luck.