Son in law

Wow - it will probably make life very difficult for your DD and will probably have a detrimental effect of your relationship with your dd and gc of she can no longer come to your home without seeing her ex-

It will also likely prevent you SIL from moving on from the divorce. How will he make new friends while living with his ILs? How will you feel if he brings a new gf back to your spare room? How will he develop his independent father role at your house?

If my parents had acted like that after my divorce I would have seen it as a betrayal

Very difficult. Hopefully sometime down the line everything will be amicable. My mother always sent cards to my ex-husband and I didn't mind at all. I wouldn't have minded him seeing her. I think we are all different. But as another poster says you have to take the side of your daughter however much you want to support your SIL. From experience though I can tell you things will level out in time.

A difficult one. It does not sound like your SIL has done anything wrong of sorts? Just your DD has decided she wants to change her lifestyle. You like your SIL and have had a good relationship with him for years. He is still the father of your grandchildren. Explain this to your DD and say you can not see him homeless. It could be said it is good of your SIL to leave the family home? Why should he?

Would depend on the circumstances my ex SIL was a serial cheat but he was still my GC's father .When my daughter divorced him we helped him with the move his new home .My daughter and her new husband gave him a job and we took the photographs at his second wedding .
Its good to be civilised especially if children are involved and in your case your SIL isn't to blame

I would be very careful on your plan, what if your daughter sees it as you are on his side? (With the limited amount of info you gave us)

What does he think of your offer? Please do not make it about you (you cannot see him in a bedsit)

Honestly, a 33 year old will manage and wont be homeless.
He will be ok

No. I would support my child. It might work for you but it might sour your relationship with your daughter irrevocably.