To be fair to the OP, she did say that there have been other issues with thoughtlessness in her first post.
From what I remember of my own birthdays, sometimes my Mum baked the cake, sometimes my Grandma (my Dad's Mother) would bake them.
My grandma was something of a cake expert and made wedding cakes as a sort of home business, my Mum made normal cakes. In later years my Granddad got in on the act and made some pretty spectacular chocolate and coffee cakes. But I believe they always offered or waited to be asked before they made the cake.
I don't think you are being unreasonable OP. You knew nothing of this tradition, but even if you did, it's up to you and your DH to continue traditions or find new ones for yourselves and your child.
When DS turned one we had three parties. Long story, we didn't want three parties but you know how these things can get out of control with families involved. Some people were available on the day, other people weren't available until the weekend, we'd already been invited to other first birthday parties and felt we had to reciprocate. The house was only so big so couldn't fit them all in at once anyway.
And at the party DH's parents came to, they cut the birthday cake and ate it. They said they hadn't realised what it was. It was a massive great cake, at a child's birthday party, with a big candle shaped like a 1 and some more candles that spelled out DS's name. Covered in a balloon pattern and with a big 'happy birthday' ribbon around it. All of which they removed so they could cut the cake. So we didn't get to sing around it or have DS blow out the candles. We were shocked at the time, they seemed offended that we were shocked.
That was the upside of having three parties I suppose, what went wrong at one party went better at the other two. 
OP my best advice is to be clear about what you want. Your MIL shouldn't have assumed that she could carry on this tradition without speaking to you and your DH first. You don't just turn up at a party with your own cake and expect it to be the birthday cake.
MIL did react negatively to the OP's cake though, she sulked through the party, didn't interact much with the OP's child, and left early. She might have been upset by the disagreement but it also sounds like she was sulking because she didn't get her own way.