I found a Bob cat kit in my backyard!?

So me and my sister are at our summer house for our vacation and we were outside starring at the stars when we hard this crying from over by a fallen tree that my dad cut down for our wood-burning fire place. We found this kitten Bobcat kit and I’m really not sure what to do. Our female cat that recently gave birth just went over there and took it inside with her newborn litter! Is it okay to leave him with our cats? or should we just throw it back outside? I know it will die soon because it is around 50 degrees outside and I know allot of predators that would find little gizmo tasty (my sister named him) So far the bobcat is suckling on our cat but I’m worried that her milk doesn’t have what he needs to survive. We live far up in the moutons so it’d take two days for animal control or a wildlife place to come and get it. Plus I’m only 17 and a half and my car is out of gas. I really don’t want to watch him die but I also know my sister would beg my mother to keep him and I think it’s Illegal to own Bobcats or something.