That’s a very tricky situation.
Overall, I would not correct the form in front of the trainer or client.
Courtesy towards the other trainer goes out the window when you (the outsider) correct another trainer. Managers should do this (and it would be best if this was done in private).
Also, since you don’t work in the facility, why should the client listen to you? Did the client ask for your opinion?
As The Rock would say ‘know your role…’