Poor gaelicsheep, this sounds just like me when DD was very small. I only have one (so no wonder you are struggling with two) but you must look after yourself - I ended up terribly anaemic through just not eating properly. I was pretty skinny pre-pregnancy and ended up stupidly skinny within a few weeks of giving birth, not because I didn't want to eat but somehow I just couldn't find the time. And DD didn't get on with slings until she could sit up independently so I know how difficult that can be.
My recommendations are:
Cheese. Babybels are easy and I bet your DS likes them too, and three or four of those while doing a feed is a good hefty injection of calcium and protein and calories that will be slowly released (rather than something like toast or a biscuit which is quickly released as energy and will prob leave you feeling a bit crap half an hour later). But Babybels are expensive if convenient so could your DH chop you up some slices or sticks of cheese to leave in the fridge for the day? Just grab a few whenever you pass. I know that your milk will be fine whatever you eat, but all the calcium that goes into it will be coming out of your body - bones and teeth - so it's an important one to keep up.
In the same vein, drinking yoghurt is fab, ditto chocolate milk or hot chocolate made with full fat milk and Nesquik or similar.
Sainsburys do really nice full fat yoghurts in lovely flavours (rhubarb, plum, honey and ginger etc) which are beautifully calorific at 200 cals per tub compared to the low-fat kind. They're on special offer at the moment - 4 for £2 or something, can't remember exact details.
Slices of (nice) ham or other cooked meat. Buy several packs when you go shopping and have one slice when you pass the fridge. Just roll it up and eat it like a biscuit. You're probably looking at 200+ calories per slice (just checked on a packet in the fridge) if you get it thick cut. And you need the iron in meat. Three slices of ham and two yoghurts (breakfast and whenever) take you to a thousand calories a day.
Pasta salad with lots of mayo.
Toast with peanut butter (if no allergy worries) and jam. You could get cashew butter if you have worries about peanuts.
Porridge with full fat milk and a handful of chopped fruit or raisins plus golden syrup/honey/brown sugar for breakfast - you can make it in the microwave so although you have to have a hand free to eat it and stir it before you put it in, it's really fairly low-maintenance.
Avocadoes - full of iron and really easy - just cut in half, add salad dressing and scoop. Or peel and chop and add salad dressing if that's easier, it probably is.
I don't know what DS eats but I'm betting it's better than toast and crusts so whatever he eats, you eat it too. And have twice the amount he does.
I got an insulated cup and put a smoothie in it with a few ice cubes made with a carton of smoothie from the supermarket and greek yoghurt. It's delicious, really good for you, and v easy. And if your cup is insulated it stays cool and delicious for a while. But you could always stick the cup in the fridge if you can't drink it all in one go.
Good luck, I know how horrible not eating can make you feel.