GoldenAge - Did you not see the post by Jenpax that said "Thanks both, yes my role is watching the children while she goes to the appointment. I have already told her that she will need to have a different appointment time in future weeks and she has agreed, but she was offered this as a *non negotiable* first step and we both felt she should take it. "
It doesn't really matter where you work, and what happens in your practice. In this instance, Jenpax's daughter has no choice but to accept this appointment.
Jenpax - I feel for you, being in this very uncomfortable situation.
But it seems that your oldest daughter (and son in law) are calling all the shots here. They probably feel that because they have taken you into their home, that you are under obligation to them. Plus, they have become comfortably reliant upon you with the childcare you are providing for them.
They don't want you to miss taking their children to one class, they don't want you moving out and renting somewhere until your own property is sold, and now they are accusing you of emotional abuse because you want to help your other daughter. There's a definite imbalance of "power" here.
As has been said above, your youngest daughter's medical needs of course should take priority over your granddaughters' class. If it is vital that they attend, then on this one occasion their father can take them, or their mother could arrange to leave work a little earlier than usual and use a taxi and take them herself.
So to answer your question - no, you are definitely NOT being unreasonable. Your oldest daughter and son-in-law are.
Good Morning Saturday 3rd June 2023