I just don't have the energy to deal with two furious toddlers
That's your main problem - and the rest would be far far easier to solve of you cracked that one first :)
I fed my twins to 2yr6mo and 2yr9mo respectively, so I know what it feels like to be completely touched-out. You want to be on your own, in a big white bed for 20 hours straight, right?
Your youngest is now over two, and is feeding for comfort only. I think that's great, and entirely worthwhile, but not if it is driving you to extreme thoughts.
My first step would be to go away or a night. Completely away, out of the house to somewhere with a big white bed, preferably and leave your DH to it. At 26 months and 3 years, your DH can explain and console and cuddle and cosleep to get through the night. You will get a rest. If it is at all possible, I'd make this a regular event - weekly? Fortnightly? Even monthly would help you regain your sanity.
When you've had a bit more sleep, and are feeling less like the only one who can take on the night time responsibilities, you might find you have the energy and resolve to start distracting from the boob demands during the day. Go out a lot, but to places like shopping centres and parks rather than confined places like soft-play, and when DC starts pestering, explain 'mummy's busy at the moment. I'll be done in a minute and we'll find somewhere to sit'. Then go somewhere super exciting (toy shop? Slide? Lunch?) so they forget. Repeat, a lot, and you'll get it so DC will accept 'not now' and you can control the frequency and location of feeds. Don't let them pull your clothes (don't sit/bend down!) - just keep moving and doing things and they'll give up eventually.
Making these changes needs you to get some sleep first. If your tired and/or depressed, it will be too hard to resist sitting down and feeding, even when you are then crying through the feed because you don't want to be doing it. You need some rest, independence and investment in yourself before you'll be able to do it. It is not a crime to invest in you - tell DH you need some time away from the DC and go for a walk, get your hair cut, go out for lunch with a book. I money is a problem, Bella Italia take tesco clubcard points for food (not drinks), so for £2.50 worth of points and the price of a soft drink you can have their £9.95 two course menu and a drink :)
Good luck. You have done and are doing an amazing thing for your DC - the only way to keep up that brilliant, close relationship now is to have regular short periods when you're not with them! They'll manage just fine with DH and you will start to feel in control again.