I'm not clear. What happens if 21 guests appear? Are they not admited to the pool or will they end up having to pay an entrance fee? Does the 20 limit include you and your DD?
Is there a party area with tables and it only has seating for 20 guests? If that's an issue, just throw out beach towels on the ground and let your DD and a couple of her guests sit on the towels when having the food.
This might be a safety issue and not allowed by the venue. Also some places have rooms with a restricted occupancy level.
OP -- double check with the venue. They did say that you could order extra food, so it does sound like it's okay if other people show up. You'll just have to pay extra for whatever is outside of their package deal.
Gently saying, sometimes I'm confused about the rules but that's only because I didn't ask the questions in the right way or thought I did and they misunderstood. (Like you asking about extra food and guests, but not about seating at the tables.)
Also, you mentioned that the entrance guest list that they will have is limited to 20 people . . . that's the amount of people they cover in your package. You could have an extra list at the front desk saying "I will pay extra for these people" that way there is no confusion that these people are actually part of your party and you don't have to be at the front desk with cash in hand.
I know this because I've held parties for more than the package deal included.
The venues I had were very accommodating, but we had everything spelled out up front. All the "What if's" were taken care of.
Write out a list of questions/suggestions/concerns . . . no matter how petty they might seem and call the venue back.
I would hate to invite 25 people and have a problem with the venue at the time of the party if all 25 show up.
The other thing to consider is . . . how old is your DD? Will some parents want to stay? (I'm not saying that you need to pay for the parents and they most definitely should not eat the kids food . . . but will there be space enough in the room for extra adults?)
Good luck and have fun with it! Hopefully the party planner at your pool will be extremely helpful.