I don't think this is about the birthday party for a child. i think it's about the tension in the family.
So if I understand you, your boyfriend's grandmother and pseudo-mother wants to give your not-yet-born child a birthday party a year from now. You're worried that your baby will get spoiled and expect 2 parties forever? First off, if no one comes from that side of the family, it won't be a big party. Grandma will either be hurt or will find it was a manageable party to give. And why is this up for discussion a year ahead of time? She could give up on the idea by then, for all you know.
So why if your child gets 2 sets of cupcakes and a few presents? If she's talking about 50 people with pony rides and a bounce house, then that's not good for a 1 year old. So you take the pack & play and put him in another room for a nap, saying he's wiped out and an't handle the chaos. But why tell her now that it's no good?
Can you say more about why you turned down the baby shower? Does she give terrible parties? Or did you know ahead of time that no one would come from that side?
Let her give the party for a few family members and your boyfriend, and let her feel like a grandma. If your family will come to her house, great - your child can benefit from having at least some relatives who get along.
You give your own party for your child's little friends (which won't happen until he's 4 or 5 because they don't "get it" before then), or for your family if they can't come to the boyfriend's grandmother's house. But I hope they would.
What causes problems for kids is one large party of 25 kids and a zillion people creating chaos and a ton of presents they can't keep track of. It doesn't cause a problem if he has a few people at her house and a few people at your house. And if she gets tired after one year and doesn't want to do it again, no harm done. If she does it for a few years and he comes to expect it, you have plenty of time to do your job as a parent to teach him to be grateful for small things and not to demand that it wasn't enough. You use that same parenting philosophy for all the occasions when kids nag for this toy and that, for when their Santa List looks like the inventory at Toys R Us, and any time they start to act greedy. But you don't deprive him of a little love that would also make an old lady - someone very important to your boyfriend - a little happier.