hmmm Had a very similar situation with my Dad. He spoiled the crap outta my son (bless his heart)... but when I'd tell my son no, he couldn't do something and my dad would turn around and say, "Oh, it's ok" and let him, it would make my blood simmer. It was never anything huge or serious, but it was the point about me making rules and my son needing to learn to listen.
I finally had to tell my Dad that he was making my job really hard. And he needed to support my decisions, not countermine them. It was a hard talk to have, honestly, because I knew he meant well. Anyway, he respected my wishes and stood behind me from then on. Love my Dad! And my son and he to this day have the most spectacular relationship. =)
Anyway... GB, she's your baby. You get to decide what is appropriate and what isn't. And when someone steps outside of those boundaries you have every right to make it clear that what they did doesn't work. Mom or not.
Ideally the subject could be approached without the heat, but sometimes that just doesn't work out.
I suggest you call her and apologize for the way the argument got out of hand, which is a good thing to do. You can be sincere about that but still remain firm in your stance about about what you think is appropriate for your daughter. And you can tell her that too.
Usually after the tempers have cooled both sides are a bit more ready to listen to the other. =) Hopefully this is the case between you two.
Z