After reading the thread, I think that the cake/no cake thing is kind of a red herring in this situation.
Basically, what you have here is a MIL who has very different boundaries than you do and isn't shy about sticking her nose in, and a husband who (having grown up with those different boundaries) isn't always on the same page as you and doesn't always recognize when you want him to check in to make sure the two of you can present a united front.
On the big parenting issues, I think you are absolutely reasonable to expect your DH to know to check, and to give no firm answers to anyone until he has. That's what gives the two of you the space and privacy to get on the same page before giving any firm information to others.
But on the smaller parenting issues, I think you both have an equal responsibility to check in.
In this case, I think you could have avoided the snit if your MIL had let you know that your DH had already said it was okay. Since she didn't, and since your DH didn't mention it (I agree with the person upthread who said he probably just didn't think of it), I think it's fair for you to ask your MIL if she's already talked to DH, or for you to say that you need to talk to DH before you can really talk to her. I suspect that if you'd known your DH had already said it was okay, your answers might have been somewhat different. You also would have been able to talk to your DH about your reservations, and either convince him or be convinced, so that your MIL didn't have the ability to complain about you later.
Essentially, you can't change your MIL (and I know you know that). You can't even really change your DH. What you can do is model the behavior that you are asking him to work towards, and then use that to reinforce the idea that you both have to check in with each other when it comes to your MIL and your children.
If you both make it an automatic question, "Did you talk to Slarti/DH already?" then you'll probably end up with fewer arguments and fewer snits.