I have had similar situations before but today took my daughters to our local arts and community centre because DD2 had homework which included "go to an art gallery and write about what you saw, your favourite picture etc." I checked the website which said it closed at 5.00, so I picked up DD1 from her friend's at 4.30 and went over there.
It's not like a big museum, it's just a single large exhibition room which has different artists or groups of artists each week, and can easily be looked around in 10-15 minutes.
We arrived there at 4.45, and as we were heading into the gallery room the lady on the reception desk called out, "Sorry, we're just closing". I said, "Oh it closes at 5 doesn't it?" She replied "Yes but we're just getting ready to close now." So I said "Well we'll only be a few minutes" and carried on. Then after about 30 seconds the person invigilating the exhibition (possibly but not definitely the artist) also came over and said, "We're closing" I just said, "Yes, I know, thanks" and carried on looking at the pictures for a few more minutes, discussing them with the kids.
Now, I'm sorry but if the closing time is 5.00pm I think it's really rude to try to chuck people out before that. It's a free centre, so okay we are not paying anything to use it but the person that works there is employed not a volunteer so as I see it she is paid until 5.00pm. If the artist in residence is bored of looking at her own pictures all day, tough.
I also run classes in the centre so am there a lot (and pay them quite a lot of money!) though this particular reception person didn't know me. So I know that there is no major 'closing down procedure' which is going to take them ages, they just switch off the lights and lock up, and she could easily have switched off and closed everything in the rest of the centre while we looked round this one room.
Not quite the same but I was similarly annoyed at Diggerland recently when it said it closed at 5.00 but when we tried to get on a ride at 4.50, we were told that the rides had closed. So effectively it closes at 4.45 then? Then say that on your literature. At the Merlin parks, if you get in a queue for a ride by the published closing time you are allowed to get on the ride before you leave.