Please keep in mind that your BIL likely has an opinion of you formed by your sister's words and actions. The same will go for your her kids - they'll hear her words about you.
I'm NC with all 3 of my siblings. My eldest nephews I'm still in contact with, but my niece, who I was close too, now has exactly the same opinion of me that her mother does.
You need to think about you, and your family unit first and foremost. Yes, it would be lovely to keep a relationship with your nieces or nephews, but you also need to be very honest with yourself about the chances of your sister allowing that to happen.
You also mentioned that your BIL and your DH were close - can you see that continuing now that your DH realises that your sister and BIL have been actively excluding you, him and your children?
Your sister has been lying to people for years that means it looks to the outside world that you've NEVER made the effort to go to your niece's birthday party... Either your BIL knows that you have been excluded or he believes that - do you think the relationship will be salvagable?
these are things you need to brace yourself for.
Also, before you contact your estranged sister please think very carefully about what you want, and about what you are ready to hear, and most importantly about how you'll feel if she simply refuses to speak to you.
It's easy to say "I'd do this..." or "You should do that..." but this is your life and you have to live with this. I spoke to my eldest brother too soon on the advice of other people and I was nowhere near ready for what he had to say. You need to do things to your own timetable.