Should I ask for child support??

My sister and my nephew have the worst relationship, she often calls the police on him for no reason, in my opinion. Last year, on fathers day he was arrested and taken to juvie, she said he hit her but I don't believe it because he is not that type of kid, he did punch a hole in the wall so they believed her. When he got out of juvie he came to live with me, 3 hours away from his mom, for half of the school year. He was doing so well here with me, he was in counseling, getting good grades and making friends. He wanted to stay with me but she guilted him into going back with her , telling him his siblings were going to be homeless because of him, she is on government assistance for housing, he is the oldest of 4. While he was staying with me she didn't help us out at all, I bought him school supplies and clothes and of course fed him without any help at all from his mom. I told him that if he ever wanted to come back my door would always be open. Today he texted me telling me he wants to take me up on my offer for him to live with us. I would never turn him down, however since he has moved back with his mom I have had a baby and money is tight. I will make it work either way but would I be in the right to asked for child support? It would only be a few months that he would be living with me before turning 18. He would not come until December when he finishes military school. He turns 18 in March.