Don't expect them to obey verbal instructions - at two, their language development is really not there for communication yet. They are learning and it's important to talk to them of course, but in terms of communicating, especially things you want him to do/not do, physical presence is worth 1000 words (and the more words you use, the more you dilute your message.) Reasoning and verbal instruction starts to work better from about 3-4 years onwards. At two, less talk more touch.
What you say about him behaving better when he can have dedicated one to one attention makes sense because you'll probably be physically closer to him. I appreciate that's tricky with a baby too so some ways to think around this -
Can you control the environment more - if he wants to get every single toy out, massively reduce the number of toys which are available so this isn't a problem. Block off, remove, or lock away things which he is not supposed to touch. When you go out, contain him (buggy/car/sling/backpack reins) until you get to where you want to go and only then let him free. Choose locations based on them being toddler safe. Getting out in general is really good (I always think toddlers are like dogs and benefit from a daily walk).
Understanding object play/schema play helps a huge amount IMO - when they are getting into all the stuff you would rather they didn't, it's because that's how they are exploring the world and learning. If you can work out what schema they are in (google play schemas) then you can give them loads of activities relating to that and it should hopefully keep them out of trouble.
Agree with sling for baby. I had the Boba Air which is great because it folds up really small. And it helps too to set up an area e.g. sofa + coffee table where you can do some activities one handed while holding the baby and have a set of activities to do here. Or some "remote games" to play with 2yo - getting them to run around and point to things of different colours was a fun game in our house, a good precursor to i-Spy. Saying different animals and the 2yo pretends to be each animal. Playing songs like freeze dance or the floor is lava. If you can invite a very slightly older friend over e.g. 3yo, they will often be better at knowing the rules for these things and the 2yo can copy (also you'll have company and another pair of adult hands).
Safe space (e.g. playpen) for baby to chill out in is also good - we had all kinds of ridiculous things like a swing inside the playpen! Just whatever will keep the baby happy while not being in arms, and also not so easy to reach for the toddler.
I found it useful to roughly have an idea of toddler/baby schedule and know which would be trickier and which would be more chilled times and tried to "tank up" the toddler with more attention during the more chilled times. Also barely did any housework during the day with two at home. Only when DH was home.
TV is also your friend IMO, especially when everyone is ratty.
If the toddler is getting in the baby's space try showing him things he can do e.g. put on a dance for the baby and make up all kinds of things like oh look she waved her arm that means she likes it. Make sure you "tell off" the baby as well e.g. if the baby flails her arm at the 2yo tell her "No, don't hit, be gentle!" even though of course she won't understand and it isn't on purpose. It's for the 2yo's benefit. Likewise when you are busy with the toddler, tell the baby (for the toddler's benefit) "Don't worry little one, I'll be with you in a moment, I'm just helping big brother and then I'll come to you. You need to wait." If he wants a toy that the baby has, try getting him to come and offer the baby another toy first. She will drop the toy she has and then he is free to take it. We found that really useful going forward into the baby being more active.