First, I'm so glad the cancer test was negative! Whatever happens with your sister and niece, I hope you move forward with joy!
I agree with the poster who suggested that your niece was probably more upset about how much fell on her mum's shoulders than anything else. I doubt she cares that much about why you were estranged from your own mum, she's probably just concerned about hers. I don't think it was her place to say anything. If your sister had a problem with it, IMO, it was up to her to speak up.
And yes, I suspect your sister's worried that you're now expecting her to help care for you. If nothing else, you might want to let her know you're cancer-free.
As others have said, it might be a good idea to let her know that you would like a closer relationship again. Her reply (or lack of one) will let you know where to go next. If she complains about your not helping out with your mum, I think it would be a good idea to acknowledge that this made it hard for her and apologize for that. But don't try to explain your estrangement - she's too likely to argue or brush off your explanation.
Another option would be to pull back and see if sister moves forward. I'm not saying to stop the exchange of birthday cards or Christmas gifts, but just, perhaps, to stop calling or texting, etc. for a while and see what happens. By "a while," I mean at least 6 months. Perhaps you'll suddenly hear from sis even if it's only to find out where you are.
Which option you choose is up to you, of course. Good luck, whatever you decide to do! And please continue enjoying wife with that great DH of yours!