sounds good on paper but in real life it will effect the relationship. I've seen it happen for years and over smaller things.
5 weeks after a c is a pretty long time. A lot of women go back to work after 6 weeks, and heck on here people are always telling women oh you can go to Disney a month after a c! Why is Disney any different?
You have clearly never had a c-section. I've had three, let me clear some things up for you.
1. The first C-section usually heals quickly. The exception to this is if there are complications, which she said she had.
2. Every subsequent C-section takes longer to heal. Every one of them. After my third I couldn't walk for a full 10 days. I was forbidden to drive for a full 6 weeks. And the post-partum is much harder due to the pain meds. And you bleed for over a month, which is lovely when you are going to a formal occasion.
3. There is a BIG difference between going back to your (usual) job, near your home, where people know and support you, and traveling to a high stress family event. I can honestly say that I have never been able to feel normal at any long-distance family event.
Not to mention the fact that she might be breastfeeding at 5 weeks and may not feel much like sitting through a formal wedding either lactating or minding a poopy/napping/screaming newborn.
Under no circumstances should the OP go to this wedding if she doesn't want to just because she's being bullied. Especially if she hasn't even gotten an invitation. If her family does not consider the birth of her child an important event in their lives, then she is under no obligation to consider her sister's legally joining with someone an important event in her own life.
Nicely tell them you can't make it, wish them the best, send a few hundred bucks and keep in touch. Time heals all wounds, whether from C-sections or from hurt feelings.