I feel your pain, my boys had the same age gap and they aren't sleepers. They are now 5 and 7, they still aren't great but it's a holiday compared to how it was. My husband also worked at night, it was down to me...
Disclaimer; as with all advice, take it or leave it. Do what works for you, these are not the answers, just things that helped me! Nod and smile at all advice and cherry pick what you fancy.
Tips to get through the day...
Be kind to yourself, you are doing a great job. All those people posting constant photos on Fb about the amazing experiences they are having, they are only showing the good stuff. Imagine if they posted every time their children watched CBeebies!
Have you got a park nearby? My godsend was totally wearing them out. A park is great because you can sit and they can run themselves ragged (well not the 16mnth old but they will tire themselves out.)
We went before tea and after tea sometimes, sometimes just a walk round the block, all weather.
It's about breaking the cycle, the more you knacker them out the more they will sleep, the more energy they will have to do it again, to knacker themselves out etc but it will be tough to start with though, as you say, you are tired too.
Swimming is amazing.
No sleep after 3 if you can help it.
Don't beat yourself up about some CBeebies time, but they love books too and you feel like you've given quality time as well. Libraries are great.
Play dates with people who feel the same, not mums who seem to have it all, parents who need a good chat are amazing!
Kids have much lower expectations about fun stuff. I mean, they can have so much fun with a cardboard box it's unreal. Don't feel you have to go to a play farm every day. Just sit and draw with them for a bit.
Try and lower your household expectations, mine were already rock bottom, so I had no problem with that!
This is much longer than I thought I would write but I am avoiding the washing. You are doing great; this too shall pass!