Families are tricky. Stepfamilies are even trickier. I don't know very much about your situation.

I could see my self in your wife's situation. I only have a young daughter, but depending on the circumstances, someday when she has a baby, I would probably love to have her and my grandchild living with me. I had absolutely no help when my daughter was born. My husband worked 80 hours per week.
A grandmother who could help with childcare would have been heavensent, especially since I had unexpected injuries resulting from labor and delivery..
If my daughter has a husband, however, what he was like would be a factor. Maybe I couldn't tolerate the situation. I would have to weigh it carefully.
I guess if all 3 were living with me, I would either want them to pay a proportionate share of the expenses OR pay a small amount with the understanding that the expense money they are saving by living with me goes into savings for their future. Whether it's a house of their own, future rent for an apartment, or my grandchild's college account.

As long as I am alive, my daughter has a home with me. No questions asked. However, in living with me as an adult, she must also exercise responsibility. If she doesn't and I don't insist that would violate MY responsibility as a parent.
Again, I don't know your whole situation, but that is just my take.
Hope it works out for all of you.
Meta