There is a truth in the saying "you don't own a name", that said names are important.
That's why, as parents we often agonise after the names we give our children,
There are names I love but could have never named a child of mine because of the emotional response I feel to that name - a bully at school, a name that evokes a distressing event or even the name of a much loved recently deceased family member (too raw).
The point is as much as no one has a claim on a name, it's emotive.
So if your SIL has said this is the "name" if you use it, is not necessarily a case of they will get over it in time. Every single time that name is used it provokes a memory.
So my suggestion is to be upfront.
Speak to her about it. She might be ok. Otherwise pick another name.
Also take into account how you might feel when your child is born.
DH and I had a name for our son, but when he was born and we held him it just didn't seem right. Neither of us can explain it - but that want not his name and despite lots of discussions prior to the birth we ended up with a name we'd both previously ruled out because it felt right when we met him 
So perhaps keep an open mind, but I'd definitely caution against using the name you want without asking and their blessing.