I find this difficult to respond to.
I suffer from depression and anxiety (including agoraphobia) and maybe at times I appeared like this. If she has issues like mine then she does value your friendship, and doesn't want to be rude but she just finds going out and social situations too stressful to be companionable at the moment. If she has agoraphobia or social phobia etc then she may have spent the entire walk in a state of internal panic which would explain her lack of responiveness.
I understand that she's not much fun to be around right now. Maybe she's just quiet and you're a bad match because of little in common.
You could drop attempts at friendship if you don't feel there's a point anymore, that its a one sided friendship. You could continue to see her occasionally and just accept that right now this is what she's going through and she might not change, and just be there for her when you can spare the time and look for more satisfying friendships with other people who are more fun.
FWIW reading what you've said it comes across rather judgey criticising her as a mother and wife, when you don't necessarily understand why she is the way she is or how difficult what she's going through is. I'd be extremely hurt in her shoes, and its the sort of thing that set me back (because it confirmed my fears that others were judging me, which made me feel more rejected and avoid contact with everyone further).
I think there's a line between being concerned about someone and so offering support and trying to make them be someone they aren't (or aren't ready to be). If you keep showing her you want to fix her then it confirms her self belief that she's broken.
Its so hard because even having been through something like this from the other side, I would find it difficult to tell you where the line is. I've had friends who have been great, supportive and friendly and I eventually did more with them and family who were too pushy and I still feel 'unsafe' around. (though to be fair the family might have been the same people that made me feel so anxious in the first place).
My best friend smokes. I think its bad for her and am concerned for her health. She knows I'd rather she didn't smoke. She says that she wants to give up some day especially when she decides to have children. She can't smoke around me (because I'm asthmatic, was pregnant, now have a baby with me at all times). But we don't talk about smoking every time I see her. I can't give up for her. I understand that giving up smoking is difficult and I empathise with her not just getting on and giving up even though it makes logical and financial sense. I love her to bits even though she does something I ultimately think is wrong for her.
The point is, our friends are human and have problems that we can see from the outside are damaging them, but we can't live their lives for them. We have to be empathetic that problems are more complex than they could appear to an outsider. We can offer support, but too much pressure would be nagging and damage the friendship.
I guess you have to either accept her as she is and that anxiety is a debilitating problem for her right now and let her know that you'll support her if or when she wants to go out more (by accompanying her, suggesting things etc) but give it a rest until she's ready. Or you decide that her problem has gotten in the way of everything that made her a good friend and that you just have to leave her to it.
I realise that Depression and Anxiety can make someone so focused on surviving themselves, that they may not be a good friend to you, of course you have needs of your friends too, I'm not saying you have to martyr yourself to be friends with her, just trying to get across how hard these conditions can be.