How would you deal with this?

"Why are you so interested?"
"Didn't we talk about this last time? Nothing's really changed. How is YOUR family? What's new in your life?"
"Oh, I'm here to get away from the boring stuff in my life and see some beautiful things outdoors! Do you happen to know what kind of tree that is? It's lovely, isn't it?"
"Everything is fine with me. How are things in your life?"
"My daughter? Why on earth do you want to know?"
"I hope you'll forgive me, but I really don't like talking about my family, even with my very closest friends. It's a real boundary I have."
"I didn't come here to talk about that; let's not get into it."
"I'm not comfortable with your questions. I'm not sure why you're asking me these things."
"I tell you what, let's not get into that again. Let's just enjoy the peace in nature--that's what I came for, not jabbering about my boring old family and friends."
"My daughter? Oh, I'm sorry to interrupt but I've just noticed what a pretty jumper you have on. Where did you get it?" (Ask her about something she's wearing.) "Where do you shop for clothes, or do you use catalogs? My favorite shops are . . . Where do you shop for food? Are the prices good?" Just get her talking about herself and what she buys. Drag other people into the conversation: "We were talking about food prices. Where do YOU shop?"

She sounds dreadful.

not wanting to be rude is making you upset and vulnerable.
i think some of this social conditioning is causing life to be burdensome.
why are you so worried about being rude to her.
she doesn't care about how you feel.
just tell her to pluck off.

You could be more assertive so avoid discussions about personal things be persistent and change conversation. Talk about the walk you are doing birds you hope to see. Groups often form clique's and there is often a nosey one. Who will get bored eventually get the message and stop asking questions.

Don’t allow someone to invade your personal space and spoil your walk. It’s good for your well being which I am certain will help you deal with your family situation. I know I have been in that situation myself some years ago. Release yourself from the stress and deal with it the sooner the better.

Good grief. I'm astonished that anyone could be so rude and intrusive! The perfect solution to dealing with this woman and her nosey pals is to simply leave the group. After all, why would you want to be part of a group that treats you like this?

If you want to continue with the group then just prepare yourself for the next round, after all forewarned is forearmed. You know she will be interrogating you so get ready to throw some missiles back. Say 'oh you don't want to know all that boring stuff about me. Tell me about your family, I'm sure they are much more interesting' or 'tell me what you've been watching on TV' (hopefully something you can discuss) or 'tell me whether you have any other hobbies apart from walking' You get the gist. Turn the conversation over to you interrogating her. Whatever question she fires at you just fire one back instead.

Or tell you you just want a quiet walk and no conversation. Don't let her talk to you.

If you can't do this then you will find it impossible to sidestep her questions. But whatever you do don't tell her another thing about your family. The nosey old bag has upset you enough and found out too much already, so zip your mouth closed on anything to do with the family, just leave her longing for it.

It could be an amusing game if you're up for it, but it seems as though it's upsetting you, and as you said the walking is for peace and retreat. So unless you're up for a battle of wits then I would just drop out and tell the group leader why you've been forced out. It might make them think.