My ex-girlfriend is like this. She always likes to have an affair with other men, and then she often makes physical contact. I think yours is still better, and mine is even more unacceptable. Although I am also a frequent visitor to the gym, I also know more about the personal education in the gym, because they often collude with girls to practice and often touch their legs on the grounds of giving personal education to girls. It is said that it makes them feel that their muscles are exerting strength, but I think it is just playing hooligans aboveboard, so if my girlfriend is like this, I still can't accept it. I will break up with her at the speed of light.
But I think you can still communicate well with your girlfriend. There is no need to keep using personal training for fitness. I don't know about the gym in your place, but our private education here is for money. I don't know if you are really rich, but I think it's enough if the personal trainer tells you how to use the equipment and how to exert your strength. There is no need to use personal training every time you go to the gym.
And I think no matter what the reason, girls must behave themselves after having a boyfriend. If they just exchange some fitness knowledge and skills with the personal trainer, I think it's ok, but if the personal trainer gropes around, I think this boyfriend is abnormal.