I could be totally off the mark here and this is not meant in a horrible or accusatory way, but do you think that part of the problem is because she has her own relationship with T1? She knows him in a completely different way and gets to see a complete different side of him that you won’t ever get to see? Could there be some jealousy there or you feel threatened by their relationship? Perhaps unconsciously you self sabotage her (admittedly poor) attempts to connect with you so T1 has to show her he knows you best and that allows you to show T2 that you have a great relationship with him. Like I said I could be way off the mark, but just some suggestions to think about as I know it would probably be how I would react!
Also when T1 said he thought you would benefit from a female mentor, do you know what outcomes and goals he wanted you to achieve by seeing her? You don’t have to say on here, but knowing what that looks like might give you a different focus rather than getting in to things that potentially have huge triggers.
So sorry you’re finding things so hard at the moment.