As a long-time volunteer, I would hope your advice would be taken seriously and if I were you, I'd be advising the staff that they need to eject such people from the premises asap and develop a regular policy on the matter, if they don't already have one. NO ONE should have to endure being called names and being harassed and stalked around a museum for any reason whatsoever.
I had an encounter with an SS mom yesterday evening. I was meeting up with DH after work for dinner since our power went out and I didn't want to sit my 33 week pregnant self in an unair-conditioned house in the extreme heat the DC area is experiencing (luckily it was back on by the time we went home).
I was in the waiting area of the restaurant entertaining myself on my tablet (which DH had just given me Monday for my birthday), and there were a few people waiting for their pick-up orders (Famous Daves).
A mother (SS) and her son (B), who was probably around 7 I'd guess, sat near me.
I'll paraphrase since I don't recall the conversation exactly, but this is basically what happened:
B: I'm bored!
SS: It'll just be another 10 minutes
B: I'm bored now!
SS: That lady there has a toy - go see if she'll share
B (comes up me): Excuse me! My mom says you should share your toy with me
Me (startled, because I didn't think the mom was talking about me in regards to a toy): Um, no, I'm sorry. This isn't a toy - it's expensive, and I don't let other people use it.
B: You're supposed to share!
SS: Come on! He's bored, and that thing can keep him entertained *Gives significant look to my belly* You'll see soon enough.
SS: Come back over here B, that mean <female dog> isn't nice, and won't share. I feel sorry for her future kid.
Me (probably shouldn't have engaged the crazy, but I'm hormonal): My kid won't be taught to be entitled to other people's possessions and I won't expect the world to entertain her.
SS: <female dog>
Me: Thank you for the compliment
B started throwing a tantrum and SS kept talking about me under her breathe, and then started complaining about me to another woman seated nearby (they didn't seem to be waiting together, she appeared to be a stranger). What boggled my mind is that the other woman agreed that I was selfish and rude to not entertain the kid, and it was my fault he was throwing a tantrum. Luckily, DH arrived shortly after and we were seated.
I had a similar thing happen with my Ipad mini at a museum...except the mom came up and told me that her kid wanted a "turn" and that since "Museums are for kids, I needed to give it to him" When I refused she tried to take it and then called me a few choice names and stormed off saying "We'll see about this!"
The staff member she got to deal with it informed her that it was indeed my personal property, no they couldn't make me give it to the kid, and no the museum was not just for kids. I thought the woman's head would spin when the staff member called me by name and told her that I was a long time volunteer. The woman and her kid spent the rest of my visit following me and calling me a female dog and a child hater.
I can assure you that if I had been the victim, I would have asked what the staff was going to do about this anti-social behavior. If they did not throw her out, I would never return to this museum ever and I'd make sure everyone I knew was aware that the museum permitted this behavior to go on inside their doors.
I am surprised that the museum didn't kick that mother out after she started following you. I would have reported her behavior for sure, that's all kinds of wrong.
As for parents demanding that others hand over their expensive equipment to entertain their children, this is something I worry about as a costumer/cosplayer.
Some of my props cost a lot of money (I've got lightsabers with soundboards that would cost over $300 to replace), and some have had a LOT of work put into building them. Now, I've been known to let calm, responsible people hold them if they ask politely. But I've also declined when I felt that the person asking was the sort who might be a problem. Either they might abuse it, try to run off, or do something stupid with it and get me into trouble along with them (It might be deemed my fault because the prop belonged to me, and the incident would not have happened if I had kept it in my own hand.)
At the moment I'm working on a lightsaber/katana style weapon. It's going to have a full soundboard with a ton of features. Seriously, I'll be able to easily cycle through nine different fully customized sound/blade effect/blade color settings just by pushing a button. I've also got illuminated switches and ostrich leg skin for the handle, it's going to be gorgeous. Now, there are some people who I would happily let hold it, mainly friends or other mature costumers or prop builders, or fans. People who understand how valuable these kinds of things are. But there's a ton of entitled parents out there who think that anything Star Wars or costume related must be for kids, or that all people in costume are the equivalent of paid mascots, whose job it is to be their personal floor show.
So for me, a grabby parent expecting me to hand over a one of a kind prop worth several hundred dollars so that their kid can "play" with it is a distinct possibility. I think I'd use the line somebody else here suggested- "Are you willing to give me a $1000 damage deposit in case anything happens? No? Well then, no touchy!"
Or perhaps "Look lady, this is a one-of-a-kind professional level prop. You want your kid to have a lightsaber? I hear WalMart sells them nice and cheap!"
I love how some people's response to this sort of BS is "Well, you shouldn't have your expensive prop/ipad/other belongings out in public, then! I had some twit say that to me once, when she ran over the hem of my cloak with her stroller (it had slipped off my shoulders a bit and the hem must have been trailing a bit. "Don't want it damaged, then You shouldn't have it out!"
(The evil side of me wonders how that twit would have reacted if somebody dumped ketchup on her white shirt? "Don't want your nice shirt ruined? Your fault for wearing it out!")
EX-cuse me!? Since when do us decent people have to refrain from using or wearing our own property, because some entitlement poisoned knuckledraggers can't entertain their own kids or otherwise mind their manners?