You really aren't so shit at this. It is HARD. I have a 2y11 month and 10 month old so I was you about 8 months ago. It is HARD.
Tips:
Persevere with the carrier, maybe try a different one - eBay/Vinted second hand - mine were much happier in an ergo baby one that a bjorn.
Use the tv. Baby's nap time = tv time . It's not forever. It's about weighing up the pros and cons. I also found that having the tv on helped because when 2 year old makes a sudden noise, it's less of a jump when there's already tv noise, as opposed to silence then a sudden scream.
Persevere with a buggy - double buggy? Fast paced walk to start with to get baby to sleep then you can let toddler out to walk and go a bit slower. Same with the carrier. Toddler in buggy, power walk with baby in carrier to the park, then once baby is asleep you can let toddler out to play.
Also. I know you say they're all different, but sleep is sleep, if baby is tired enough, they WILL fall asleep in carrier/buggy even if you're walking slowly.
It is SO hard, but it gets easier. I did gentle sleep training at 6 months and baby now sleeps in the cot for all naps so it's not long, you have options.
Overriding all of this, please please do not leave a 2 y old when you can't see them. Anything can happen. Even in a play pen, a piece of a toy could break off and they put it in their mouth and choke. It's just far too risky. Also, after 2 or 3 times he will just seek you out to be near to you anyway so it's counter productive