I think you've gotten some good advice (especially the point about not calling her an "extra").
Just be honest. Your sentences about how she's family and you're upset to let her go, she's been great for all of you, etc... but you have to make some changes, all sound genuine and gracious. Be generous w/ severance if you can and definitely let her know that you have ideas for some leads, want to help her find her next position, will give an amazing recommendation, etc...
She might be upset initially but it sounds like you're very genuine and hopefully the trusting, caring relationship goes both ways.
Good luck.