Why can't I choose to stop sharing my iCloud+ Keychain (passwords) on Family Sharing?

If you sign in on a device then it essentially makes it "yours" and gets configured with everything that you do with your iCloud items. In theory you would have completely erased the device before using it and then done the same afterward.

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

I only did this once with a device that deliberately had not been erased and when I signed into various services it asked me if I wished to delete existing data from the previous user for those services. I don't think I use iCloud keychain at all myself so that didn't make any difference but I was asked to keep the old photos on the device for a while and there I said yes, keep them. For other things I said no.

I think your first bullet point is your answer. Your passwords synced to her phone (and then to everything she used with iCloud) when it had your ID on it. The only way to get them off is to ask her to hand delete them --> How to find saved passwords and passkeys on your iPhone - Apple Support

Some background questions:

1) Do you indeed have different AppleIDs?

2) Did you completely sign-out of her phone; and is she signed-in w/ her AppleID?

3) Is the device listed on “your” AppleID or “hers?” (determined by logging-in at https://appleid.apple.com/ )