There's only so much you can do, so just handle the greater need first. If one DC has to wail for a minute while you tend to the other, remember: "This is where they learn life lessons like how to share and wait their turn”.
Try to get your eldest to nap in the afternoon when you baby naps. When the baby’s napping and he’s quiet too, don’t do housework! Just sit and space out. Stare at a wall. Listen to music. Close your eyes. Read a magazine.
If you didn’t get a bath seat for your first child, then make sure you definitely get one for your second! It means you have your hands free so that you can wash your baby and your toddler at the same time.
Save yourself from traipsing up and down the stairs with both kids in tow and get a changing station for each floor of your home. Buy a really cheap changing mat and stash it underneath your sofa to keep things tidy.
Try to involve your toddler in caring for your baby if you can. He might be able to help you out with nappy changes by passing you the wet wipes or a new nappy. My toddler was surprisingly helpful. He entertained the baby, and got stuff when I was stuck on the sofa nursing. His chatter and questions also made for interesting conversations.
Put together a ‘busy box’ with some toys which will occupy your toddler when you’re feeding your baby.
Consider getting a high chair which supports a newborn so you can put the baby in it without worrying about your toddler poking its eyes out. Useful when you need to pee.
Get a thermos mug so you can have a hot drink before it cools down to room temperature!
When you wonder why you ever had your children so close together, don’t forget to step back and focus on the positives of a small age gap. There are lots, trust me, but that’s another thread!