The appropriate person to escort the mother of the child would be her spouse if she is married. If she is not married then the next adult family member would be appropriate, or any adult that she is close to.
I assume your husband is divorced from the child’s mother and if that relationship is not good since the split, then funerals are not the right time to put anyone in a role that would be upsetting, especially the immediate family of the deceased. The important thing to remember is that the funeral is for the child’s family to grieve as well as celebrate the child’s life, and so decisions about who does what should be made with respect to what will be most comforting to the parents during this difficult time.