Mom's doggy day care raises hackles
You should consider very carefully the value of this service before complaining about it.
All the same, it is definitely a breach to have someone redecorate your house. Assuming that Betty is creating busy-work while she's with the dogs (and is not suffering with a cognitive illness), I hope you can say to her, "Betty, can I bring up one issue? It drives me a little crazy when we come home and the cabinets and furniture are rearranged. I know it might look like a mess to you, but things here are the way we want them." (Also, given that she has a key to the house, you should secure any personal documents or items you don't want her to have access to.)
If you want to decline this daily effort, say: "Thank you so much for your kindness, but we can't accept it any longer. We're truly appreciative, but now we need to make a change." And then you can send Betty to me.
Dear Amy: Why do people send wedding and shower invitations, and then tell you what gifts to give?
In my day, people had manners.
Some of these brides and grooms have parents who are just as bad. These people find your address, somehow, but you've never met them, and they don't get in touch with you otherwise. My solution: Ignore these invitations. There is no excuse for bad manners.
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Dear Disgusted: You're right. There is no excuse for bad manners. So -- let's do you.
You're a bit unclear about the circumstances surrounding this deluge of invitations from near-strangers, but ignoring an invitation is not a solution -- it is rude and inconsiderate. You need not feel pressured to give a gift if you are not attending, and so you can safely ignore registries or suggestions.
Surely, back in the day (when people had manners), they knew to always politely RSVP to an invitation, regardless of the invitation's source.