As far as the idea of ironing out the kinks in the passagio, an exercise my singing teacher does with me helps. My weak spot is slightly above yours (and has moved up there as a result of two years of lessons, I think), so I do this exercise starting on an Eb, but you might want to start from something lower, possibly a Bb?
He calls it a foghorn. Starting somewhere around middle C sing Oooh and slide smoothly up an octave, singing all the notes in between, hit the note at the top and come down again. Do this until you're comfortable (or in my case can do it without giggling) Then do the same thing going from what was the top note last time and doing another octave up. Then do two-octave foghorns from the first starting point. Then go down to a low note (in my case Eb below middle C) and do one and two octaves. Then finally go as low as you can, and do as long a foghorn as you can (in my case 3 octaves).
Then collapse in a giggling heap......
The idea is that you are probably going to need to change voice at least once during each foghorn. You work at it until the change is smooth and controlled.
As far as belief goes, I think this is something all we late starter ladies struggle with. We've all been there - singing "second" because we can read music, migrating to alto when that term is first used, without knowing that it implies a lower voice, and not developing the upper range until having lessons when we are taken by surprise at how far up we can reach. Finding that the migration from back row of the choir to soloist makes one conspicuous and self-conscious, and hesitating to put ourselves forward as that's not how we've been brought up.....
The only answer is, I think, to sing wherever and whenever you can. Choirs, workshops, courses, concerts - anything you can join or gatecrash so that you build your confidence and your experience of your "new" voice. Well, that's what I'm trying anyway
Cheers
katyjay