We have something similar in our house. For me I think it is either my husbands bio-mom, whom passed when he was 8y, and/or his brother who passed a week before we bought the house (across the street from the house where he lived).
Ghosts that travel with you can attach to things. For 'mom', I think she arrived when the Aunt gave us her wedding dress and a box of stuff that had been hers. For BIL, he arrived when his son wore his favorite jacket, one that he'd been wearing that day, to the house and left it. The jacket left and he didn't. We were the family that he got along with, so...
For me I try to take it in stride, and talk to my kids 4y (the sensitive one) and 10y about it. The 4y is always playing by herself, but carrying on conversation like she's chatting with someone. She now has a new playmate named 'Posty' that comes and goes, and there have been others.
Hubby is completely freaks when stuff happens. This past week has been bad. We had to install dreamcatchers in the kids rooms because the 4y had mean people in her dreams. Last night, hubby felt someone grab his feet like they were trying to wake him up for something, but no one was there.
Anyway, for your picture problem I would do three things.
1. When the pictures fall, just have your kids pick the picture up and set it at your spot at the kitchen table. No words or reasons needed.
2. When you put the picture back up, just say outloud 'gee, I sure wish these would stop falling down'. or 'gee, I sure wish I knew why these kept falling, the little one is wishes it would stay put.'
3. Move the pictures that fall from hanging on the wall to being in standing frames on a shelf or bookcase. Or even just put them in a photo book. Maybe your SIL is mad at your MIL and doesn't want to see her pic.
I think the purpose is to not make a big deal about it. It is what it is. Maybe watching the movie 'The Sixth Sense' would help?
Good luck.
M.