OK Burnt, it sounds like you are very sure about what you want to do. So below are some ideas for things you can do with your baby and toddler...
Bear in mind that they do need almost constant attention at that age. The whingeing occurs because that is the most exciting thing happening for them at that moment. :( If you turn your attention to them fully, they won't whinge.
You can expect maybe 5-10 mins uninterrupted, a few times a day if you're lucky. Plus one longer period if you work hard to synchronise their naps and you are very, very lucky.
It is difficult and tiring to do this all day long. It feels hard because it is hard. It is harder if you are depressed (as you already know). It is easier if you get a break from them and can come back 'fresh' (because your partner or another relative has them for a bit, or they are at a childminder's). It is, funnily enough, less hard the more you throw yourself into it. If you can really have fun and play, it will be easier :)
Also remember that mostly all the baby wants at that age is you. S/he will be happy doing more or less anything you do with your 2 year old, if s/he is in a sling or on your lap.
Everyday chores: give the baby a clean duster to suck play with 
, or stick him/her in a sling. The 2yo can sweep with a dustpan and brush; help with the hoover; wipe surfaces; clean the bath by climbing in it; pick up; hanging up clothes; wash pots and plastic things, etc. The trick is to turn it all into a game. Put on some bouncy music while you do it. We often used to listen to while we did jobs.
Cooking together: the baby can prob just bang pots and smear . The 2 year old can 'help' with quite a bit: mixing; rolling pastry and bashing dough; putting toppings on a pizza or pastry slice; cutting cheese and mushrooms and other soft stuff with a butter knife, etc...
Playdough: play with it: chop it, roll it, make models, use the machines that extrude it in sausages... If you make your own using a recipe like this one you can be confident that when the baby puts it in his/her mouth, it won't poison him/her :)
Finger paints: spread the kitchen floor with a plastic sheet or loads of newspaper. Get paints, brushes and paper. Prepare for mess!
Singing songs with hand actions: Wheels on the Bus, Incy Wincy Spider, Wind the Bobbin Up, etc. There used to be collections like The Singing Kettle when mine were young, so if you feel daft singing by yourself or you don't know songs, you can sing along to a video. But you must sing!
Dance: the more wildly the better!
Make music: good instruments for littlies are recorders, whistles, harmonica, drums, some xylophones... Basically, anything you bash or blow! You can make your own.
Megablocks/Duplo: build things!
Dens: take the sofa apart and make a den with its cushions, and with blankets/throws/sheets/towels/the clothes rack, etc. Hide in it together.
Watch toddler TV together. It's not a cop-out, if you do it together. Talk about it all as you watch, eg: "Oh what IS she doing now?! Look, she's riding a bike!" Anything you say - literally anything - is OK! And it is also not a sin to use the TV for a short break (like your very own in-house childminder!) if you need a breather - which you will!
Cutting and sticking: with child-proof scissors and a stick glue like pritt-stik. Different coloured sheets of paper are best. ELC sells craft packs. Not all are suitable for younger children, but some are.
Drawing - crayons and chunky pens.
Puppets: buy them or make them (from cardboard, paper plates, socks,etc.) and put on a show.
Water play: have a bath together or fill the kitchen sink (clear the draining board); use sponges, plastic cups to pour, empty bottles to squirt, etc.
Mud play: put on wellies and go out and jump in puddles!
Bubbles: you can blow them anywhere. I recommend the small tubs with the wands that are easier for little fingers to hold, and that contain less liquid when it spills.
Dressing up: you don't need special outfits. Your 2yo will love trying on your clothes, and dad's! You can make crowns and other accessories from cardboard. etc.
Explore: make every trip out into an expedition - even just to the local shops. Look for leaves and mini-beasts and conkers and snails and anything.
Have adventures: If you're comfortable with make-believe, have expeditions to the arctic or the jungle or other imaginary places: eg. the buses are elephants and the dogs are tigers! (MY friend and I once had a fantastic hour in the park with our kids on a dragon hunt! We found dragon poo and everything!)
Right... That should keep you occupied tomorrow!
(If you do a google search for 'toddler play', you'll find more ideas).
(I could say a lot about what I think of your DH, but I'll restrain myself. I would like to tell you, though, that I have raised 2 kids all by myself for years on £16-24K. We do fine. :) )