I'm Im traveling from New York to the Texas Passport Agency since its the only place with appointments available before my flight (Feb 17th.) The appointment is Feb 15th. Will I be able to get my daughters passport the same day?

Yes, you can obtain your passport the same day. They will process and print it and have it back typically just after lunch on the same day with applicable fees.

Only if you have an appointment correct?

Actually you get it the same day you're talkin about the Mickey Leland Federal Building downtown very efficient wonderful people everything is so orderly nothing like chaotic New York and I'm from New York I know how chaotic everything is in New York