Oh OP. I really, really feel for you. I recognise the anxious, obsessive feelings you are having in myself. Anxiety is an absolute bitch and can latch on to things and make them feel like HUGE deals even if we know objectively they are not.
I would gently encourage you to get some therapy, in order to unpack the way you feel about yourself and also your difficult family relationships. I think your own mother did you a lot of damage, from your posts.
I do want to reassure you that you are NOT a bad person. You are not defined by things you did in the past. You didn't hurt anyone (except yourself!), you showed an unusually high level of remorse by actually reporting yourself. Every person on the planet makes mistakes, most of us do things we aren't proud of. It's part of what makes us human.
However, if you're anything like me, I'm not sure that reassurance will help. I think sometimes with anxiety we can crave reassurance, trying to settle our minds - although it can give temporary relief, at the end of the day it doesn't make the feelings go away and if anything just compounds the problem. We need more and more reassurance to feel ok about ourselves. It's a cycle and a trap.
If my Mum had told me something like this as an adult I wouldn't have batted an eyelid and it certainly wouldn't have changed how I felt about her. I would just have felt sad for her, that she'd allowed this thing to make her feel so guilty and ashamed for so long. Your daughter clearly loves you and wants to spend time with you (as she wants to go traveling with her Mum! That's lovely). Please book your trip, visas permitting (I know nothing about that but I'm sure it's easy to clarify) and enjoy every second.