D.B.
Your SIL has only 1 successful relationship with a man - and that's with her brother. She has no self-discipline, so she can't discipline her own children. She loses her temper and curses at them, which isn't going to do anything except teach them to lose their own tempers. Wait until she gets the first calls from school because her little ones are swearing and teaching the other kids the "f" word.
Your husband should be supportive of his sister, and that means giving her a break now and then. I don't understand why you can't have the kids over to your house on occasion. Is there a reason you haven't seen them in months? Is she avoiding you because she knows you disapprove? Are you not inviting them because your husband is overly involved all the time? If she swears, even once, in your home, your husband needs to take her out on the porch and tell her to stop or he's packing her 3 kids in the car and sending all 4 of them home.
He also needs to get her into a parenting class so she can learn some skills with discipline. A lot of us grew up with "just wait until your father gets home" which taught us that our mothers had no power or authority - and we had to fight that image of women as we grew up. Your nephews have it even worse - "just wait until I call your uncle" - so they have no respect for their mother. The situation just escalates. At this point, your SIL is completely ineffective and undisciplined, and she can/must learn to stand on her own two feet.
If he reaches out to her on HIS schedule (meaning your family schedule) and her calls aren't just when she's in need of something, you won't feel so imposed upon. If you have scheduled family get-togethers, it will feel like an invitation for the cousins to play and get together, and those 3 kids can see a family the way it's supposed to operate, with kids getting gentle and constant guidance.
And your husband should not participate in or encourage any guilt trips when his sister calls her dad to get him involved. And how is it that you and your husband even know she calls? Is their dad calling your husband to relay this message? Then Grandpa needs to knock it off.
Both uncle and grandfather can be positive role models in the children's lives, and that's important when their own fathers are nowhere. But that means teaching everyone to stand on their own feet and not responding to mama's whining or sob story.