Without getting too analytical by reading too into your question.
I think I understand. I have loving support from someone yet feel as though someone who is related to me depends on me, this is not a child though, which would make the answer more difficult.
I handle it like a balancing act, I do the best I can. If I can't get something done or can't be there for the person, in the way they might need me, at a certain time. I tell them and why. I am honest with the person who needed me, if I have moments where I need some loving support. Sometimes I can put my problems aside and treat each of them individually. Sometimes I can't.
If a child were involved I would make sure I had time for myself in some way. I would need to be at my best to keep some sanity. Although I have no children that would be my plan.