>you're basically my therapist

I know she wasn't being completely literal here, but that's extremely unhealthy. Parents should not treat their children like therapists. It damages the relationship, and it puts the child in an unfair position.

Sounds like you handled it pretty well. I'd make sure she knows not to talk about your relationship like that, in the future. Also, let her know that you're happy with your relationship and that should be enough for her.

The other stuff isn't on you. It's her own feelings of jealousy for her sibling, and her own self-worth issues. She thinks a parent's success is based solely on their child's success, and that the child's success is based on how physically attractive their partner is. That's a whole load of issues, right there.

In her head, she imagines that people will judge you for your partner's appearance (which you seem fine with), and therefore will judge her for it. In other words, if your partner isn't hot, she must be a bad mother. I don't know what you can do about that.

If she's like this a lot, consider pushing her towards therapy, or lowering the level of contact you have.

If she's not normally like this, make sure there isn't some other thing going on. Ask her why she feels jealous, and if it has to do with her relationship with her sibling.