2 year olds don't respond very well to verbal instruction. That doesn't mean don't give it, but don't expect it to be effective, it's all really for practice. Basically you want to back up every single word you say with a physical action, like carrying him somewhere, blocking access to things, presenting (shoes etc) to him, leading him to something. Don't give him a choice unless it's a real choice (so the choices you suggest are good, but don't say things like "Right shall we get our shoes on now?" if you don't intend it as an option.)
Control the environment (ie, babyproof) rather than relying on telling him not to do things, I also find it helps to separate stuff out so e.g. do nappy and getting dressed first thing on waking, rather than trying to do that at the point of leaving the house. And predictability helps too e.g. if you always get dressed first thing, that's much more predictable for them than if you sometimes let them watch TV first, sometimes want to get ready immediately, sometimes do a bit of a slower start etc.
Pre-warning CAN help (but might be confusing). Remember they don't really understand time very well yet, so 5 min warnings are less helpful than giving something like "After this Peppa Pig, it's time to get our shoes on" or "We have to go home soon, you have time for three more slides or a go on the swing, which would you like?" (And then count down the three together). Try narrating stuff with now and next like "Now we're going to eat breakfast and you can watch 2 Peppa Pig, then we will get dressed and then we'll go to the shops".
And YY their physical needs feed in hugely to their mood - so lots of small, regular snacks and drinks can help and trying to ensure he gets enough sleep and some fresh air/exercise every day. They are a bit like dogs in that sense.
"The problem is" is great (it's from How To Talk, isn't it?) but I think it's a bit wordy for a 2yo, and might be frustrating him further.
I also think it's useful to conceptualise that it's not your job to convince him to agree or be happy about everything that has to be done, it's just your job to make sure it gets done. So sometimes you'll be able to give him a choice of shoes vs wellies and this will work brilliantly, sometimes you'll be the shoe-putting-on-robot which will be his favourite game ever, and sometimes you'll strap him into the buggy and shove the shoes into the basket to put on when he's stopped flailing madly.
2 is also a very strong age for "I do it myself!" but they tend to be a bit shit at doing things at first so a lot of people take over (especially if the child gets easily frustrated). It can actually be quite helpful to encourage them to try themselves, give them space to work through frustration, encourage them with phrases like "ooh that's so tough, you're doing so well" help them only with the "tricky bit" rather than totally taking over, allowing a bit more time for them to try things themselves and not being perfectionist over whether or not they get it right, as long as it essentially works. They will get better at this kind of thing over time and then they are more able to be independent at 3 or 4.
If you have a very grumpy easily upset child, it can help to keep a kind of mental note of whether it's better/worse at certain times of day, and adjust expectations based on that (e.g. try to centre the times when you're asking more of them on their "best time" of day and have fewer expectations of them during their more volatile times).