When you're surrounded by people who are incapable of giving genuine love, it's so easy to conclude that you are unlovable. I would challenge the idea though that there is such a thing as an unlovable person. There are only unloving people...people who are unskilled at giving love.
T1 hurt you terribly by leading you on the way she did. But I would contend that her lack of consistency is greater evidence of her lack of love for you than saying that she can't be your mother and can't love you enough to undo past damage. I believe she may FEEL love towards you, but her actions show she's incapable of truly GIVING you love. A good and loving therapist knows how to give love appropriately in a therapeutic way, that is, in a way that heals rather than harms.
My T has never said she loves me. She's never even said she LIKED me. And yet I believe beyond a shadow of a doubt that she does love me. Not that she feels warm feelings towards me all the time (I doubt she does) or that she needs me for some reason, but that she is COMMITTED to doing what is needed to help me heal. To me, that commitment is worth more than all the affection in the entire world. To me that is one of the truest forms of love.
LG, look around at the people in your life and ask yourself who has behaved responsibly towards you. Who has consistently helped you in the most effective and appropriate fashion? Who has always supported you? Who has taken responsibility for their mistakes and done their best to repair them? Who has been there consistently through thick and thin? THOSE are the people who really love you, because they are people who are truly capable of love. The rest may feel all kinds of wonderful feelings about you, but if they're not competent at being loving, it isn't going to help one bit.
I think for you, this may actually go beyond love to belonging. You want to feel that you BELONG to someone or some group of people. Because you can be loved without having to belong. I can lovingly dispense advice to people on the internet without requiring them to become permanent fixtures in my life. I think T1 was appealing to your need to belong by telling you to think of her as a mother. But it's no good belonging to people who don't know how to love well. You might feel a little better just feeling like you belong, but such people will always hurt you more than they help. So the first step is to let go of attachments to people who can never love you in the way you need. And the second step is to find people who CAN love you properly. After you learn how to identify people who are really capable of giving love, then you'll able to find some who you also feel you belong with. And then both needs will be met. I trust that it will happen for you, sooner or later.