Penona - reason probably doesn't work for years but talking still sometimes works, I know DD understood far more than I realised at 12 mos.
DD used to go MAD at having her nappy changed, in fact any kind of being messed with activity. I reckon it's a control thing.
Toddlers spend their whole day having things done to them, and even if we give them choices between breakfast cereals, t-shirts or toys to play with, adults make all the decisions.
And they have so much more knowledge than ability. How frustrating must that be? I recikon DD started her proper paddies when she realised that as soon as she started to be able to walk to/reach things, we started putting them out of the way, taking things away and saying 'no'. You spend yer whole life looking at those stairs and thinking how great it wil be when you can climb them, and then as soon as you can, Bam, stair gate goes up. Bloody hell, I'd have thrown a strop too.
Penona, is your DD able to get involved in the putting away activity as a game? May be worth a try although no promises it'll work!
And the nappy thing, well, I had to resort to trapping her sideways under one leg to change her. The strops lasted until she decided it was more fun to lie down for me to do it, than have a wrestling match that I always won. Oh, and making nappy changing a whole load of fun once I got her pinned to the mat helped too - tickling, singing, raspberry blowing, book reading, silly faces, ridiculous over-cheerfulness til you're ready to burst a blood vessel, brought out all the big guns til she got the message.
Drives you nuts though, doesn't it?
The playgroup thing sounds like intense disappointment that it had to stop. Not unreasonable really to express an emotion, but a pain in the arse to deal with when you have a howling child and everyone's staring at you!