meals: is the important thing that the child should sit in a seat designated by the parent at certain times of day, or is the imprtant thing the actual sustenance? if the latter, may i suggest carpet picnics? much more likely to try things if it's a fun game and you aren't physically constrained. lots of finger food. spread a tablecloth to catch spills. Provide a variety of foods and let child eat what they want. If you can't control what you put in your own mouth, what can you control?
nappies: depending on the problem, there are a million solutions to this which don't involve a screasming child. Including: mobile nappy changes (put something v interesting on a table. Child stands to investigate it. FRom behind, you whip the nappy off and clean up), having a shower to sluice away the poo - if child wants, they can get in the shower in their clothes and take them off in the shower, going for a swim and taking the nappy off and cleaning it as an incidental thing, ditto paddling pool in summer, leave them out of nappies for a while (advocates of Elimination Communication would be v. supoportive of this, but it's not something I ever got into seriously), a washing-up bowl of water with bubbles to investigate, and put the child in that to clean their bottom. Some of these will be too crazy for you, some might really help.
"having tantrums over small things like getting him dressed, telling him no he can't go up the stairs or whatever?"
Some children go through a phase where it's easiest to get them dressed the night before after the bath. OR even once they've gone to sleep, in that heavy heavy floppy deep sleep stage.
Why can't your child go upstairs? Surely that's something you want him to be able to do? When he starts on the stairs, you say to yourself that now it's stair climbing time, and you go with and stand behind so he doesn't fall, and count stairs with him. What's more valuable than that?
"the car seat"
Take the bus or walk home from nursery. Or climb in the car and sit together in the front for 15 minutes having a welcome-back-mummy cuddle, and letting your child "drive" and then when they are ready, they'll go in the seat with something really interesting to look at. What they really want is your touch and your attention after a day at nursery, isn't it? Where's the law that says the joyous reunion has to wait while you drive home?
There's always ways to avoid tantrums and conflict. They usually involve allowing time, parent being playful, and not getting hung up on things happening the way YOU want rather than the way the child wants, which is usually just as valid.