You have my sympathies op, I've got a 5 month old and a 21 month old and it is fucking HARD!
My main tools are distraction and questions/challenges- 'hey, look at this bug, shall we see if we can find anymore this way? Do you think we'll find a spider or a ladybird?', 'hey, that's a cool leaf shall we take it home and show it to daddy', 'do you want to have a snack? Can you climb into the pram? and then you can sit and have it there', 'are you going to take (toy) to brush your teeth? Will you brush toys teeth too?' And so on.. all said in a cheery voice, and with praise when she's compliant. Obviously it doesn't always work, or I have to try a bunch of different questions before she's distracted enough but the majority of the time it works eventually (and I do not have the patience for it to take ages so I'm not having to do this stuff for more than like 5 minutes at most).
I feel like my life is spent managing her mood/behaviour, while also constantly holding/feeding/entertaining a very fussy baby and it is full on. Honestly I've felt better in myself since I accepted this is just my life right now and I have to deal with it the best I can (and often my best isn't great, but it's my best). I felt like I was fighting it for a good while and it was making it harder and making me resentful, less patient and desperate to escape. Which also made it harder to implement the distractions etc, because I just didn't want to HAVE TO. But I do feel like that's how life is with a toddler, you just have to 🤷♀️ (I have an older dc so have been through toddlerhood before).
Most of our outings are to groups at our local children's centre because it is a child friendly, contained space and there's usually volunteers who will help on occasion/keep an eye on toddler if you need to tend to baby. On the days where we don't get out I feel a lot worse in myself and am less patient etc. so I try to get out every day, even if it's just for a walk.
I know you've gotten frustrated at the pram comments but im going to mention them too. When Ds was born I didn't intend to have a double buggy but about 4 weeks in I realised it would make my life so much harder not having one and I got one. You've said your boot isn't big enough - perhaps there's one out there that would fit in your boot. Maybe you've got enough money to buy a cheap second hand tandem that won't fit in your boot but could be used when you're going places that are within walking distance from home (obviously depends on your situation, personally a lot of the places I go I can walk to in no more that 40 minutes). Even if it's just that you get toddler in it at home and go for a walk with them both in it so you've gotten out and some fresh air and a change of scenery. That way if you don't stop anywhere to get toddler out, you don't have to try and get them back in. And make the straps tight enough that they can't get out themselves.
Have you tried white noise for baby? My son isn't a fan of the pram and will also cry if it's not moving - I have found white noise magic for getting him calm or helping him fall asleep and stay asleep. So I put the white noise on as we start walking somewhere and he'll fall asleep with the movement of the pram and then when I stop moving as long as the white noise continues he will stay asleep (the naps he has with white noise on are also always the longest naps he'll ever have, usually he'll only sleep for 15/20mins, with white noise he'll nap for anywhere between 45 minutes - 2hrs) - the occasions where the white noise has cut out for more than 10 seconds he wakes so I know it's the white noise!
I'll try and add any other tips/tricks that I use as I remember them just in case any may work for you. Wishing you well. I keep trying to remind myself (daily, multiple times 😂) that this phase WILL end!!