Wanting your gf to spend more time building her "primary" relationship with you, that is to say the relationship that you both are building a future around, versus on her "secondary" relationship with him, that is to say the relationship that is important to her but plays a less prominent role in her life, is perfectly valid. No need to feel guilty for that, as long as you're also acting with compassion and giving everyone's needs (hers in particular but perhaps genuinely his too some day especially if you and he become friends) consideration where they can be met without violating your own needs.
I agree with Rory that she needs to reconsider that whole thing of keeping you and T separate. I can see why she would be scared of getting you two together... what if you don't get along or what if you can't handle seeing them being affectionate. Or maybe she wants to keep him something special just for her, or maybe it's a holdover from the affair, feeling like things need to be a little secretive. But it's a bad plan for all involved. She's brought him into your life by asking you to accept his presence in her heart and love life. If you want to meet him and get to know him a little, which I think is healthy, you should get that chance. Ideally, you guys should get the chance to have honest, no-holds-barred, ongoing conversations as needed that can lead to greater trust and understanding all around. Is that idealistic of me to envision, especially considering the affair? Perhaps, but why not aim for it? Wanting to know his thoughts about the relationship, at the very least, is very, very reasonable.
The only boundary that you've laid out that I think might be problematic is the pda thing. Perhaps it won't be a big deal, but I know that little acts of pda make me feel very connected to my partner and I wouldn't want to give them up. Are you afraid people you mutually know will see them together and get the wrong idea?
The major players. Me, under-30 bi female. Gia, girlfriend of 3+ years. Clay, new boyfriend/dom. Davis, ex/"it's complicated."
The supporting cast. Eric, Gia's husband. Bee, Gia and Eric's toddler. Dexter, Gia's lover. Helen, Eric's lover. Izzy, Clay's partner.