Okay, question time. My nephew is only 7 weeks younger than my daughter, and for the past 4 or so…

Okay, question time. My nephew is only 7 weeks younger than my daughter, and for the past 4 or so months my sister has been living with my mom/grandparents and has basically since then (actually before that, but now it's completely) had our grandma and mom take care of her son, too the point where he can't be without them, especially my grandmother. I've been helping by staying if she ditches and go back to stay with her boyfriend for a few days, or watching him for a few ours, but she gets mad if anyone brings up the fact that she's not taking care of her child, my mom is permanently disabled due to an accident, and can't do much, so it's all on my almost 70 year old grandma with health issue, and I have tried for months to get my family to let me take him for a day or two or as long as they needed for a break, but until now they wouldn't because they said it wasn't my responsibility, but I'm starting to look into the process of becoming his guardian, because my family can't handle it, I'm scared my grandmother is gonna pass away or be hospitalized from how exhausted she is, and the same with my mom, but my sister only says I'm not the same as you (me) as a parent and doesn't see anything wrong with what she's doing... How can I go about getting her to let me have him until she gets herself taken care of, and they get stable, because this is not good on him, or my family, I just need advice?