First, it doesn't sound like you wanted your sister there. And it also doesn't sound like you did anything to help make her job easier, like cutting back on some of your kids' activities or work out carpooling with other parents from school.
Second, it's clear she didn't live up to your expectations, but she did "help" you during this time - isn't that what you asked for - some help? Due to her immaturity, difficult time in her own life and being thrown into this situation with no prep, it sounds to me like she did the best she could.
Third, maybe she wasn't the best person to come help, but guess what, SHE CAME! She was there for you and did the best she could.
I think you need to cut her some slack. And that maybe you need to reassess what it means to HELP someone in need...it shouldn't mean become you, it means to do what you can to help someone get back on their feet.
I understand that we don't know all the history and facts regarding this situation. So to answer your question, I think you should call her. I think you should thank her for everything she did. And I think that you should apologize for being so hard on her. No matter what it sounds like she was one of the only people helping you and your family when you needed it most.
You don't have to apologize for every little detail. But just saying you're sorry and you appreciated her help would go a long way towards mending your relationship. No one expects you two to be BFFs.
Try to appreciate your sisters GOOD qualities. Remember the Golden Rule - Treat others like you want to be treated.