Start of the end..

[antlers]

Since it's your day to have your daughter, go to the party, and stay in the background...just let your little one know that you're there. Be there for her.
Text her mother and say "OK, I'll see d8 on Saturday at the party then." Plan on taking the child back with you, unless she wants to stay. If she wants to go with you, then take her on your day as planned. If she wants to stay, then let d8 know it's OK, and tell her you'll pick her up on Sunday then.
Don't let the child's mom make the decision...forget your text in your above post. You make the decision. Your child's mom went ahead and made the decision, without any input from you, to schedule her party on your day to have her. Forget whether or not if she is expecting to reply...reply as I've said above. This is your decision...it's your response to a decision that she made without taking you into consideration.
Be strong for your kid. Good luck.