Another experience we had was with three haflinger ponies coming to a neighbors house to do rides, and it was much better. The ponies were very well groomed with glossy coats and shoes for walking on the cement, fitting saddles, and a handler for each plus one person to serve as a poop scooper. I had no problem whatsoever with them and even inquired about where they were from so I could drop a good comment with their boss/manager. Like I said, its all about safety and presentation.
Be ready for well meaning parents with loads of concerns and questions as well. We don't do pony rides at individual homes at my farm, but we do have them at our farm to be 'rented' for parties, and we also have pony rides at our fundraiser in October. They may ask you some very odd things or claim abuse even if your animals are not in any way harmed and you have to be very gracious and smile anyways. They don't mean to be rude usually, they just don't know.
Also, since your mare is a halflinger, you might want to think about finding a way to bring a plastic mounting block or tall step stool. It can become tiring for any horse to have to deal with children pulling in it's saddle/back constantly as they get on and off, and may upset her or make her back sore. Lessening the distance will make it much less stressful and strenuous for both you (so you don't have to give constant legs up) and your mare.
Make sure she doesn't shy away from mounting blocks or kids getting on or off wrong too. Some kids are just rediculously stubborn and won't mount or dismount correctly, even after you teach them, and your mare needs to know how to cope with them sliding off her butt, being clumsy, hanging off of her while they're scared to slide down, etc.