Is the paternal uncle's daughter entitled to reclaim the money she paid for her share in the apartment, after she agreed not to request it in the event of canceling the trip, knowing that the amount has been spent and not fully paid to the landlord?

If it was agreed with your cousin that she would share in the cost of the trip, and that she would not demand the money back if she did not travel with you for any reason, then there is no obligation to return anything to her. This is because the condition is binding upon whoever stipulated it upon themselves willingly and by choice, based on the Almighty's saying: (O you who have believed, fulfill [your] contracts), and the Prophet's (peace be upon him) saying: "Muslims are bound by their conditions." However, if you return the money, it is more befitting and better.