This is all my POV hopefully nothing too upsetting on here. Long ass post though!!
I'm currently 28 weeks pregnant. I conceived at 37 and will be 38 when she's born. I'm fully aware of how lucky I've been. We planned to start TTC after our wedding, I was 34. A few months after I was literally struck down out of nowhere with a painful vulva condition (which still isn't 100% and never fully diagnosed). No sex for us for a year and a half. The reaction down there whenever we tried was horrific.
At the same time, you have that awareness of babyness expected from you. Being in my mid thirties and the eldest of my mother's side grandchildren, it was quite accute. That expectation of being 'the first'. Whilst on the sex ban, the inevitable happened and the next oldest grandchild, my cousin, announced her pregnancy. Then another cousin. Then my little brother. Yes it hurt, but I didn't see that much of my cousins and by the time my nephew was born the plethora of babies (close friends also had theirs) was old hat and I was ok.
However if I'm being honest, there was always the hope of producing the first grandchild on my husband's side. Yes all babies are special of course they are, there is just I don't know...something about having that joy of being able to make yourself so happy and giving those closest to you the same happiness. Probably not making sense!
Anyway, this year marked DH's brothers marriage and back in January I had to have a really good think about the possibility we might not be first after all. That his siblings might continue to provide the grandchildren and years down the line, when grandkids were part and parcel; not new and exciting and shiny anymore, I might eventually limp over the finish line with a baby and everyone would be too busy to give a shit about us. There would be no big fuss, not on the kind of level the 'first' got anyway. More of a consolation style pat on the back and a 'yes well done you finally did it, what a shame it took so long'. Or, never even getting there. The heartache and the knowing that you are going to be someone that people pity.
Yes it sounds so silly written down but that's feelings for you I guess.
As I said, I'm lucky. After an ectopic last year and surgery to remove endo we finally got pregnant and I didn't have to deal with the feelings of being overtaken yet again in the baby stakes. I really don't know how I would have dealt with it; although I wouldn't have been able to avoid the baby (DH would be very supportive - but would also tell me to give my head a wobble).
But that cycle of heartache still goes on. One of my closest friends has recently had her third miscarriage. Another friend is also pregnant and due around the same time she would have been. She keeps in touch and is happy for us, but cannot see us in person, and it's so sad. She doesn't want to be apart from us but she needs to protect herself and we understand.
Anyway. Back to you OP. Given my experience I'm firmly in the do not 'just bring your baby to the party and SIL can get over herself' camp. There is a time and place to address this with SIL, however a party she has organised, albeit for your brother, is not it. She's probably confided in her friends and family about her feelings towards you and the baby. Bring that baby in and she will feel all eyes on her. Those pitying eyes. Watching her. Her reaction. Is she ok? Is she going to cry, storm out, shout, have a breakdown? Her every move now on public parade. I can't see how well that will end for anyone.
I would address it after the party, but definitely before Christmas. No public parade, no group shaming her out of her 'attitude' on WhatsApp. Just a reach out between you and her, then hopefully a talk with just you and her, no baby. Small steps. Let her know you acknowledge her hurt, but she has to find a way to cope. She might not get over it, ever or until she has her own baby. She might not want 'a hold' of yours. And she doesn't have to. All she has to work towards is being in the same room as the whole family at Christmas, and to just be civil. And that will do. In time she may change and be a wonderful aunt. Or plaster on a happy smile. The civil stage won't happen in time for the party, so work towards Christmas, hope it works out.