I know exactly what you mean. My voice movement therapy t who I worked with for a year and a half really was like a mom to me. My own mom is an alcoholic, emotionally inconsistent and not someone to confide in with emotional issues. With t, she taught me how to be ok with strong feelings, how to handle conflicts in our relationship, and she was just so supportive and present to me. She held and cuddled me when I was really upset, which is something I never got from my parents. She helped me decide to make the move to Chicago, and siad she'd support whatever I wanted to do.
Even now, though I'm not paying her (because I can't afford it!) she made up her mind to still work with me and be in touch until I get a new t. I get so much out of being able to write her and our skipe conversations every few weeks than I do talking to my mom, because I can't really be honest with her.
So yes I know about this wish. And it's magical when it can be fullfilled in a way. I never expected that, or knew I even was really emotionally without a mother until I started working with her. Now if she could just adopt me already I'd be good!