Can I solicit child support even if my babys father and I are living together?

My fiance has a 7 year old son and pays cild support but the boys mother does nothing all day long and wants more money everytime they go to court.Me and my fiance have a new baby and during my pregnancy he lost his job and wasnt able to pay so he got sent to jail.Is it possible for me to solicit child support? Everytime he gets some money he always has to send it to his sons mother because hes always afraid of going back to jail and I have has to put off getting things for my daughter because hes always sending his money to her. I want to look out for my daughter and I love him, but she deserves some of his money too. dosent she?