For Men Only-Please Advise Me?

I have been divorced for four years froma man I was never in love with. we have a granddaughter with special needs, and we are together a couple times a week to take care of her. we do spend hours together as a result of this child, and he comes to my house as he has none, he lives with his parents (another story). We are together until she goes to bed sometimes. We are NOT in love, we do NOT sleep together, there is no interest there at all, the only reason for the connection is the baby. My question is this....will I be able to have a relationship under these cirstances? Are there men who will understand this, or will I be doomed to never be trusted because of this situation? I do what I do for the baby. He left 2 years ago, but we were basically her only stability, thus my insistence that he remain in the picture for her. Any words for me?