This is a great question, and it's so thoughtful of you to come to here to find a way to help her

Is your mother comfortable talking to you about her agoraphobia? I think that would be a great place to start--agoraphobia can develop for many different reasons, so the "solution" is different depending on the person. If you can get her to open up to you about why she doesn't feel comfortable leaving the house, you can problem-solve with her and ask her if there's anything that you can do to support her. You can also offer to help her leave the house in baby steps (maybe ask her if she wants to walk up and down the street with you, accompany you to a nearby store, etc).
I can only speak from my personal experience, so this may not be applicable in her case, but it's very important to me to know that someone actively wants me to recover--it gives me an incentive to fight against agoraphobia. For me, that's a friend saying that they understand what a challenge it is for me to leave, but that they would LOVE to have me go a certain place. It helps me remember what I'm missing if agoraphobia runs my life. (When I lose this incentive, I end up becoming self-destructive and don't make an effort to push through my anxiety).
In summary--talk to her, ask her how she can help, let her know you still love her as a mother while showing her that if the two of you can work through it together, you could go back to having that great, involved relationship. What strikes me about this post is how much love and appreciation you have for her--just make sure she knows

Best of luck!