Don't overestimate how much you can get done in a day. You will be massively slowed down.
Don't leave the house to go to a park or anywhere outdoors without a buggy. Even previously reliable first borns can suddenly become bolters and you will need to put the baby, sling and all, into the buggy to chase after.
Maybe buy reins and keep them in the changing bag. Some people frown on them but they're better than a near miss with a car.
Don't underestimate how long it will take you to simply get out the door most days.
Try to get really organised about putting jackets, boots, mittens, hats, changing bag, and other outdoor stuff exactly where you'll need it all when you're trying to go somewhere.
Have a shower before your P leaves in the morning. Get him to enjoy dad and toddler time in the morning.
Wash the baby in the kitchen sink until well able to sit on his own. Don't attempt to wash both new baby and toddler in the bathtub together. You only have two hands, and babies have been known to poop in the bath. Bath time proper can be mum and me time for the toddler, or better still, dad and me time.
Be patient and mutter to yourself 'this too shall pass'.