Sounds like she's just being a teenager. As long as she has friends of her own, I wouldn't worry about a lack of 'deep' conversations. It can be embarrassing when parents try to do this.

I do think it would be good for you as well as her if you could say sorry for the past.

It's probably best to keep it light, just a quick mention when you're out shopping for clothes or have just watched a moving film about families / mothers and daughters, mentioning that you could have been a better mother, or something simple like that.

If she starts to squirm, stop!

Parents hardly ever say sorry, and I would really respect any parent who manages it.

You'll be careful, I'm sure, not to put anything onto her regarding having to 'forgive' you or console you (that's not her job).

You both sound lovely, and I hope it works out for you.