Oh dear no, of course not, this is not remotely true.
This is the normal, standard and expected reaction of a woman who was abused by a cheater for years, being honest about her vulnerability.
She said she'd feel disrespected, and that's becuse she would be being (once again) disrespected. The mistress doesn't need to be there, OP has no relationship with her, the father can simply be told no for once in his life, thus solving the problem being invented by her entitled arsehole of a father.
You cannot compare the reaction of a person who was cruelly abused and lied to's reaction with the reaction of a piece of selfish, lying shit who stuck his cock in randoms, or a woman happy to shag married men who still slags off the man's wife.
The father is a man who shags randoms and runs roughshod over other people as he pleases, attempting blackmail to get his way again. The mistress and the daughter don't get along and the mistress slags OPs mum off. These are just established facts.
So no, there is no emotional blackmail at all. Just an abused woman trying to hang onto the last shreds of her dignity, who doesn't want the woman who helped destroy her marriage to be slithering around on her daughter's special day.
And her mother also did not say she would not come but pointed out that she would be being disrespected if the mistress was given this acknowledgement.
So the mistress will just have to learn to live with the fact that she won't ever be a part of OPs life. Oh well. It's not like she cares.
I'll assume you're a cheater or the OW who enables cheating, if you continue to try to pretend not to get this.