Gees, I would definitely not allow Grandma to be a part of planning any party. She sounds like the sort who wants to make everyone happy and even tho it apparently made a lot of other people happy it didn't make you happy and you were giving the party.
I think that you can just say that you're having a sleep over for her birthday and not even mention anything else.
Why will family be disappointed? You can invite family that you enjoy being together with over for dinner or to a no-host dinner at a restaurant but you certainly shouldn't be expected to entertain everyone, especially from the step-daughter's other family. Reality is that she has 2 families now.
I had to do birthday parties differently because until my foster daughter's birth mothers parental rights were terminated the judge asked that I include one of her aunts and her family. CSD was going thru the motions of deciding who would be allowed to adopt my foster daughter.
I think around 10 was the last year my daughter had a kid's birthday party. After that she invited one friend to help her celebrate. They could have a slumber party or go out to dinner or dinner and a show, swimming and dinner, etc. I helped her plan what she wanted to do and participated with her and the friend doing it.
Doing more than that overwhelmed my daughter. She came to live with me just before her 7th bd and I invited my friends and their children to Chuck E. Cheeses. Last time for that. LOL For her 8th and 9th birthdays we did a kid party and then had a family get together with some of her birth family. My own family lived too far away but my friends helped with both the kid party and with the birth family get together. There was too much emotional baggage connected to birthdays and once I figured it out and could do it I downsized them quickly. Sounds like you're in a similar situation with birth family. You now know what won't work for you.
I think it was her 10th birthday that we had a kid's party in our back yard with a trampoline when she turned her ankle and spent most of the time in the ER getting a cast on it. That is when I finally caught on that birthdays get out of hand and I needed to do something different. Like your party took on a life of it's own.
When a party includes people from the "other family" it was not very much fun. When my daughter planned a 6th birthday party for her daughter and decided to invite people from her birth family including her birth mother, I told her I wouldn't attend and I think I made the right decision. Those sorts of get togethers at that time were overwhelming just in the fact that I had to be on guard the whole time to be sure that everything went smoothly. She was hurt but finally realized that I had bent over backwards to make relationships work for her and that now that she was an adult getting along with them was her responsibility. I wasn't going to be the one standing in between her and her birth mother.
My daughter has had kids parties for her children every year but since her daughter's 6th she hasn't tried getting the whole family together. This year she had a joint swimming party for her son's 7th bd and her daughter's 10th bd. The part of her birth family with kids came to the party which was great. Over the years I have gotten to know and like them. So the party included kids and parents.
My daughter said that she talked with my granddaughter who agreed that from now on her birthday will be celebrated with just one of her friends and she could choose what she wanted to do. This is the same routine that I started with my daughter's 11th birthday and it worked out well for her.
My daughter and my grandson's father are divorced. We celebrated my grandson's 1st and 2nd birthday together, our two families. Since then each family has their own parties even tho his parents and I still visit with each other from time to time. Time has healed wounds. I count my grandson's father and his parents as casual friends and would be comfortable getting together with them but it does seem to work best and in the best interest of my grandson to celebrate separately.
There is less confusion about roles this way. My ex son-in-law moved out before my grandson was 1 and so he doesn't have the experience of his parent's being together. There is no confusion about who is in charge or the adult tension that such a get together would create. His mother and father now have an amicable relationship but don't socialize together the rest of the year making separate birthdays just a continuation of the rest of the year's events.
For most families, it's unrealistic to expect the two families created by a divorce to celebrate together at a party. I don't understand your mother's way of thinking. I suggest that people get along better when they're realistic about the divorce and the fact that it's created two families for the child(ren). Pretending that everything is the same creates too much tension. The two families can get along and if......the people involved choose to socialize at other times of the year as well as for birthdays it might work but to throw people together for the one event is just not a good idea, imo.
So, celebrate your step-daughter's birthday in a way that makes you and her happy. When I was growing up our family, that lived in the same area, got together for a birthday dinner whenever it was someone's birthday. We also got together for dinner at other times, too. My aunt nearly always made the birthday cake which was applesauce with a brown sugar icing. I treasure that tradition.
My mother was often ill and so I only had one kids birthday party. I don't think my brothers ever had even one. But yet I felt treasured on my special day. Then, again, kids bd parties weren't so prevalent 60 or so years ago.