Do I allow the custodial parent to see my 4year old during summer visitations if I am traveling to their city?

Doesn't she already have some sort of visitation during your time? In TX standard possession says if parents live more than 100 miles apart NCP gets child for 6 weeks with CP getting 2 weekends during that time period. If she would allow you to have lunch/dinner while you're in town during her possession, you should allow the same for her. Your daughter will get used to being with you during the summer.