#1 take care of you and yours. Even if you run there today, when you leave she will probably end up in the same boat as she is not well. Would she come be near you? Then you could help out with kids etc but I am assuming you are not trained in counseling her. I am so glad she has you as a friend, you are very good support, Don't make this about you and create a new issue for you. Its only human to worry and feel bad for her. Many of us anxiety sufferers have also dealt with depression and know it takes huge effort to get on the path to wellness. Where is their father?
I get the worry and the feeling of responsibility its all about balance. Sorry you are having to deal with this sister, it isn't easy.
Social Services? I don't know how good they are (around here they are terribly overworked), but your friend's comments sound like she is considering harming herself. It is not your fault and should not be your sole burden, but you should contact someone in an official capacity in the place where she lives, and tell them what is going on.
You are absolutly right, you have to consider that you are a mother and you need to put your childrens' needs first. If you are concerned your friend is suicidel you need to call a family member of hers that lives close to go check on her, or call the police. She may be upset with you for talking to her family about her issues, but you have to think about what's best for her and her kids. She needs help and you are being the best friend you can be by giving it to her by contacting a family member, or law enforcement. You cannot feel like she is your responsibility entirely. You are not qualified to care for someone who is depressed and she needs help! Especially if she has kids. Do her the best favor you can and contact help. She will thank you later!