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It's an important part of building rapport. Above all, anyone in therapy should feel comfortable about the choice to continue or discontinue.
What you want for her is valid but respecting her choice is important. The thing about having family is that decisions aren't made in a vacuum, we take into consideration those we care about, but they're still for just that person to make.
Oh, I don't even analyze much. I've done therapy myself, it's actually a good thing for everyone I think.