Overall I've really enjoyed being a parent, but poor sleep has been the hardest part. At times we've both been so tired that we weren't able to think clearly about how to fix the problem, which can be very tricky. We've figured this out more over time, however, and sleep has improved with each successive kid (n=3). Here's the main things that have worked for us, all in one place.
Note that kids and parents vary a lot: our three kids are different from each other, and your kids likely even more so. I'm hoping that many things on this list will be useful to many people, but it wouldn't be surprising for several of them to be a poor fit for any individual family. I've ordered them roughly down from the ones that I think are most likely to work for anyone who tries them. Perhaps unsurprisingly this is also roughly in the order of youngest to oldest; my impression is kids diverge more over time as their personalities come out.
Sleeping in multiple rooms. If the baby waking up means only interrupting one parents sleep that's about half as much sleep deprivation.
Blackout curtains. Small children typically wake up with the sun, which means you're up to. If you can keep their room solidly dark in the morning by blocking out the sun you can shift their schedule to whenever is most convenient for you, typically a later waking.
Using a Snoo automated bassinet. It gently rocks the baby and shushes them back to sleep when they wake. We used this with our youngest for the first six months. It worked very well, and automated almost all of the helping babies fall back asleep that I needed to do with the older two. We weaned her off it much more gradually than they recommended, with first weaning mode (stops rocking after the baby is asleep) and then running it without rocking.
Sleep training. At some point they no longer need to feed as often, but either don't know how to fall back asleep on their own at the end of a sleep cycle or would enjoy getting a cuddle before going back to sleep. I wrote about our experience with our oldest, and how her naps got immediately better. With our youngest, at 15m, we've recently dropped the last night feed, and are in the process of teaching her that she needs to go back to sleep on her own the whole night.
Letting kids know when they can get up. When kids are a bit older, they'll often wake up near the end of the night and not be sure whether it's morning. An "OK to wake" light (or a janky incorrect clock) can help them figure out whether to go back to sleep or get up.
Child proofing bedrooms. When they're old enough to no longer be in a crib, it's great if their bedroom is a place that they can play unsupervised in the morning without waking you up.
Teaching them not to wake you. When they're old enough to play in the rest of the house unsupervised but still sometimes play too loudly or fight, teaching them that in the morning this isn't ok. If they wake up before us they have to resolve conflicts independently and keep their volume down; if they don't, both of go back to not being able to leave their rooms until we're up. I think the last time we needed to enforce this they were maybe 4y and 6y.
Other things that can be helpful:
If things are really not going well, and you're both way too tired to figure things out, pick one of you to get caught up on sleep while the other covers. The one that's caught up can then figure out what needs changing, and make it up the unevenness later.
Some people have had good success with cosleeping, but while we started with the two older kids sleeping in an annex cosleeper we didn't do this with the youngest; the Snoo worked better for us. We will sometimes cosleep when traveling or in other unusual situations.
Tracking wake windows can help with better naps.
Velcro swaddles are another thing that worked well for us with the first two kids. With the youngest we used Snoo-specific ones, which are a similar idea. Though they're a bit better because you can keep using them even after the kid learns to roll over, since they clip in. All three really liked being swaddled.
When doing night feeds with formula, prepare bottles ahead of time with water measured out and put a cheap microwave in the baby's room. Then when they wake up hungry you can heat up the water, add the powder, shake, and feed them relatively quickly and without waking yourself up too much.
Make the kids' beds with multiple layers: sheet, towel, repeat. Then if they wet their bed or throw up it's much faster to get everyone back to sleep.
When you need to put two kids in a double bed, consider thinking of the bed as landscape not portrait and using separate blankets.
Some people hire night nurses, someone to be responsible for the baby while you sleep. Generally people like this a lot, but it's super expensive.
When taking red-eye flights it's really worth it to stick with bringing a car seat as long as possible, because it puts them in a far more comfortable sleeping position.