Well I'm speaking as the person who's got divorced (well ok we're not actually yet - we're still just separated, but we will be once getting the divorce sorted creeps it's way to the top of the list of things I need to sort - other more pressing/urgent matters in hand at the moment).
my exH has 2 sisters living here in the UK (the other siblings and rest of his family are all in Zimbabwe still so the relationship there was very distant anyhow). They both have 2 DC each, and are my DS's only cousins.
When we first split exH was a bit funny about me maintaining contact with them of my own accord, but he soon got over it and realised that actually it wasn't doing anyone any harm. They still wanted their children to maintain a relationship with my DC - and with me.
On Sunday it was DS3's Christening, I invited both of my exSIL's and their family - unfortunately only one could come - but she did, with her 2 children. And it was reallly lovely, I got a hug from my nephew and niece before they left with a "bye Aunty FAQ". And I chatted with my exSIL just like we always did - and exH was there too, as we my parents. At one point while I was mingling with other guests I looked across and my exH, exSIL and my parents were all sat chatting together, and infact my parents and my exSIL sat at the same table throughout the celebration (although my relationship with my parents is strained at the moment - but that's an entirely different thread).
I guess it depends on how your SIL and her family want to do things/see things, but I've found that my exH's family are treating me and my DS's no differently now than from before, as far as they are concerned we are still family by virtue of the fact that we married and had children together.