I might be batteries SIL too! However my brothers children are older teens now and we have a fairly independent relationship with them and they come and stay during longer school holidays. My brother communicates and does the hand over of dc, I haven't seen or spoken to SIL for years. I was writing Christmas cards to them this evening and 9 year old DS didn't realise that his uncle had a wife
as he has no recollection of ever meeting her (possibly 9 years ago).
My brother and I were and would still be close but I actually think it is he who doesn't want the relationship. Our other brother makes a lot of effort too because he says otherwise he would never see or hear from them. My parents focus almost solely on this brother, they visit them maybe 5 times more often.
It would be easy to blame it all on SIL but I think (after 20 years of mulling this over) it is her fault only in that she is Not proactive in preventing it. My brother seems to have skipped the "it's okay to like your family" stage of development and she couldn't care less about his family (doesn't have any of her own so doesn't see the importance) rather than actively dislikes us.
Anyway OP, i cried buckets over this in the beginning but I have come to the realisation that I cannot change it so I persevere with encouraging a relationship with my nieces and nephews and my brother and accept that it is what it is. I love him, but figure it is a one way street and that's fine too. He was the baby, like batteries dh, and has a bit of an issue with us teasing him about stuff (no more than we tease each other). He is better qualified and earning than any of us but seems to have a wee chip on his shoulder about being looked down on by us (affectionately). We think the world of him but it is not reciprocated. Luckily his children are just as adorable as he was and like to be loved by us.
So, i think it is all too easy to blame the wife but his relationship is with you OP and as an adult it is his responsibly to maintain that relationship. It might be that you have to do all the work to maintain it, like I do, but that might be worth it too.