ANOTHER UPDATE
I was talking to MIL on the phone today and she mentioned "I had the last piece of Babybartfast's birthday cake today." Wait, what?
Me: "I thought you were just getting a single-serving thing."
Her: "I never actually said that, I just told [my DH] we'd get the smallest cake."
So yeah, points that came to light:
1) She bought a $25 cake which yielded six pieces
2) Every time she picked up Babybartfast from her toddler art class this summer (which was frequently, since I was home with Bittybartfast on the other side of town), the two of them would go to Baskin Robbins and get ice cream and look at the ice cream cakes and talk about birthdays and birthday cakes. I now have a pretty good idea why Babybartfast was disappointed at her cake - MIL (either explicitly or not) had primed her to expect a Baskin Robbins ice cream cake instead.
3) It wasn't just "go get ice cream" - they bought the cake and MIL brought candles and everyone in the store sang to Babybartfast before they cut the cake there in the store.
4) The big one -
DH WAS THERE at the "do-over" birthday party! I'm REALLY peeved at him for this - he knew how I felt about treating this as a replacement birthday cake, and even if he didn't agree with my stance, I think he should have stepped up and said something. Apparently it was DH, Babybartfast, MIL, and FIL all at Baskin Robbins together, and nobody thought to tell me. I assumed it was just MIL and Babybartfast and
maybe DH joining them for lunch, but DH never bothered to tell me their outing was any different than how it had been represented to me before.
Since DH was there, I can't really blame MIL for this anymore

She knew just as well as DH did how I felt, and she chose to ignore it, but DH bears more responsibility for the parenting decision IMHO and I don't blame MIL for thinking it was okay (or pretending to think it was okay - she does that a lot) when DH didn't say anything.
On the plus side, I asked what she said to Babybartfast at the party, and it was indeed along the lines of "You have to be gracious about the cake you've got" instead of promising her something else.