Does he get enough sleep? I find this age they are SO much worse if they don't.
Could there be any other underlying issues (sight/hearing etc?). Might be worth thinking about. We discovered DS was very long-sighted and needed strong glasses- not excusing his behaviour but at about this age he could be awful in the afternoons and I think some of it could have been tiredness from overstraining his eyes.
Are you expecting him to walk too far? If so, then can you go in the car/scoot etc? If not, then you could set up a consequences/reward system for walking well and make sure he knows what your expectations are. You can refuse to carry- this takes nerves of steel but is possible. Also hard if you are time pressured- I guess you are with older one, but it might be worth being late/leaving early to avoid being late once or twice to make your point re there will be no dragging or carrying, you are in charge!
He is 3.5 but if you have a long walk you could put him back in the buggy. I kept DD in the buggy last year. She has just turned 4 so was 3.5 last May. She was in the buggy for school run May, June, July as it's far enough that it wasn't easy for her to walk and I didn't want battles. The buggy went in the garage over the Summer and didn't come out again.
Re the other stuff- I didn't like the naughty step- but we did the go to your room thing (for time out) which works best for us. Touch wood we don't have to use it much at the moment (DCs are 4 and 6) but I remember a bad time when DS was 4 when he spent a fair bit of time in his room (4 minutes at a time!). They can really push their boundaries!
Do not accept any violent behaviour, it has to be crystal clear.
Re the being dry- not sure about this- maybe leave it a month or two then go for it again, but make it more his responsibility from the word go as he is older now. Have nursery got any tips on it?