Replenish your changing bag/whatever you use as soon as you get in. Then it will be ready to just pick up when you've wrestled both into their mode of transportation.
Yes, definitely get out of the house as much as possible. When feeding the baby when out, make sure that toddler is strapped into a buggy or highchair if you're not somewhere self-contained as two year olds can run FAST.
Yes to a changing station with supplies downstairs as well as up if you have more than one level.
Sticker books are useful. Top tip - remove the 'negative space' from each page so that the toddler can take the stickers off independently.
My toddler had been in nursery for two days a week, and we kept that going as I knew I was going back to work and she'd only just started there. It gave me a chance to do stuff either in or out of the house that is quicker without a toddler in tow and a break from someone standing next to me saying, 'mummy, mummy, mummy'. It also gave her a break from the baby.
I started preparing tea straight after breakfast eg chopping onions. If I did bits throughout the day, it was more or less ready to cook at tea time.
Try to keep the toddler napping during the day for as long as possible. It improves their mood as well as giving you a breather.
Get a double buggy. I didn't have one and it was a pita always having to use a sling. My toddler didn't like the baby in her buggy, so sometimes I couldn't put him down even if she was happy playing. Also useful for transporting stuff.
Cbeebies is a must. Alternate with DVDs if you like. Mine enjoyed the Clangers, Bagpuss, Peter Rabbit etc. I guess technology gives many more options now.
If you have a freezer, either batch cook and freeze meals or buy ready mades. If I had had the cash, I would have used something like All Plants for a month or so.
Online shopping also a must.