I'm sorry to hear that. I can understand his feelings (generationally speaking) and I suppose he is entitled to his opinion. He is even entitled to check in with his daughter and make sure she is happy and okay with this arrangement. But it sounds like this has crossed a line into bullying and belittleing.
I really feel bad for your wife as she clearly is hurt by this. However, she basically needs to set some boundaries with Dad. She should acknowledge him and say "Dad, I have heard and appreciate your concerns for me." Then she needs to tell him to back off in no uncertain terms. And there needs to be consequences for his actions. If he can't let it go, then she should probably put some distance there. "Dad, I told you I will no longer discuss this with you" and she should exit so he can play with the kids or she should ask him to leave. She has to put her family first, and while I am sure you are her priority, she is making things worse by letting him treat her this way.
She wants his approval, but she may not get it. That is being an adult. Part of me wants to suggest she turns the tables - "Dad, you were a great provider, but I never felt close to you because you were never home. I am so glad <hubby> IS a doting involved father."
I also think it could help if she let him know how he is affecting her. Not just that he is hurting her feelings, but that he is undermining her feelings about her stepchildren - she is "paying" for them, but it is an act of love not subservience. How dare he challenge her relationship and feelings for them? And vice versa - he should be thrilled your stepchildren have you in their lives. They are lucky.
As for you, out of respect for your wife, I think you need to be kind to her father and a role model for the kids. It is her problem to deal with, not yours. I know it is easier said than done, and I know your feelings are hurt too. But if you get angry at him or make it more of an issue, then he will be able to blame you for any distance that he is creating. They need to work it out.
So sorry you are in this situation. It sounds like you have a particularly strong partnership with your wife.
PS - As for the "fake" part. I understand your feelings, but I suspect in his own way he is trying to be respectful. I mean, his issue really is with his daughter's happiness and not with you per se. I also think you are lucky has hasn't taken to snide mutterings in front of the kids. That is standard operating procedure for some people. It stinks, but it IS between them, and I think you should be glad he isn't laying into you too :)