Kit key, mine weren't good at high chairs and trolleys either.
I'm not with some other posters that they are 'vital' though.
I insist on car seat harnesses, I can see that's vital. Perhaps because as others said, that has always been insisted upon, I don't have an issue with that. I have used the Traffic Club Books, Sammy Seatbelt to illustrate / reiterate the safety message, but beyond that have never had to physically force them, they just know it's expected.
For trolleys I managed it by not doing big grocery shops with them. My husband did it solo for a while on the weekends without myself or the kids, and now we on line shop for example.
For the buggy I let them out to walk.
Sometimes there are time constraints, but I do usually negotiate them. IE you need to sit in there until we get to X, so we're there on time, but then you can play. Or I distract with food, singing or turn the buggy to forward face, that sort of thing.
For the high chair I let them get down, table manners and asking to get down etc are for when they are older I reckon, if as a baby they've had enough, well then they've had enough!
Don't really get all this need to come out on top in a battle of wills, not giving in etc.
Some of the posts here are assuming 'giving in' to them will be a nightmare when they get to school or whatever. I haven't found that to be the case, my son's report commented on how he was sensitive to needs of others, and good at listening etc, so I'm not losing sleep over that side of things.
That's just about teaching / showing them how to respect people in my mind, which is completely different to making them do whatever you say.
So the example given earlier about the plane which was delayed because the child wouldn't put on their seat belt. For me that is not respectful to the other passengers, I wouldn't be using negotiation in that sort of situation. I have been in that situation, you do just need to get on with it in that sort of scenario.
Anyway I guess the main thing is Kitkey that it's perfectly normal to have kids like yours who don't stay still / want to get out, so don't worry you are not alone. :)
If in your case some of those things are 'vital' {for example no other way to do a shop except on your own with the kid/s in tow}, then as some others have illustrated consistency, force etc will ultimately make a difference I guess.