Many years ago I attended grad school with a woman who was a social worker. When I inquired about fostering (out of interest) she advised me to wait until my children were much older. Her reasoning was that foster kids often have special needs that take extra time and attention, and it can be alot to handle for a family who already has small ones.
Over the years of raising my sons I've come to see that that was very wise advice.
I really admire your heart to help this child. The guiding principle for me, though (and assuming you could legally do it), is "what is in the best interest of the child?" And by "child" you also HAVE to consider your own children. How will they be affected? And what about this poor child, bouncing around from parents to grandparents, and then to another family? And what about when grandma changes her mind because she got some rest, or got caught up financially, or whatever? What does that do to your children? And to this child?
I would also be careful that I didn't do this because it felt "right" thanks to your childhood. It has to be right for the *current* children involved.
Good luck.
PS: I would talk to a lawyer too.