Schools can't just leave 14 6yr olds unattended in a pool.
So the mother either had written permission via something on the invites that she was accountable for each of the 14 children left in the pool, and informed the school of this in advance, or when you say you weren't sure who else was there, the other parents were there.
So the only issue is that your child wasn't invited, and you say you fully understand why, because she and the birthday girl don't like each other.
It's an on the fence here, if it's a pool party, it seems sensible not to dry off all the children, return them to school, all separately make their way back to the pool. Put their wet costumes back on, and get back in. Actually pretty smart planning on her part.
On the other hand, your DD had to witness the rest of her class attend a party...but a party of someone she doesn't like, nor likes her, so should have had no expectation of being at.