Sorry, I don't think any of these things are rude.
1) Once you post pics on facebook, they are fair game for pretty much anything
2) These are pictures of a mutual relative. You're talking about a daughter and a granddaughter snagging pics of her parents/grandparents to incorporate into her own photo album/profile. I see absolutely nothing wrong, rude, or abnormal about that. It wouldn't cause me to think twice.
There's a good reason why people snag pics and put them into their own photo album - because then they have that picture also. If your DH took the picture of their parents down, his sister would no longer have access to it. Also, by putting it in her own photo album, her friends can see it - friends who may not be friends with your DH - this seems like a normal desire. She can also organize the pictures - she might have a family album where she keeps a lot of pictures of her parents/other family members, etc.
If your DH had emailed the whole family with the picture, saying 'gee, look what I found the other day - isn't this a great pic of mom and dad?', and someone had taken it and posted it to facebook, it would be the same thing. Totally acceptable.
Honestly, the *only* time I would ever even think for a nanosecond about something like this is if it were an artistic picture a photographer friend took. A picture of my parents that my brother posted? Or a picture of my grandparents that my uncle posted? I would consider these functionally as much mine as my brother/uncle's.