Ok read through and thought of a few things not mentioned
Kellysmom blog: the BEST in latest breast feeding research. I had it bookmarked and read things over and over. It was especially helpful in the face of some very undertrained professionals.
Foods that may help you with supply: oats, fennel supplements (after a feed), brewers yeast, fenugreek, red bush tea.
Pumping is NOT an indication of milk supply necessarily. It's a whole other skill and I sucked at. Also it's next to impossible to know how much milk they take so just do little and often if necessary and you can face it. Try a babymoon: a day on your dressing gown, no bra and little one ticked in there witha gro, open and no vest. They can feed whenever and the skin to skin will help you both feel better and increase supply. Even though I was ragged at the time, I kind of miss my baby moon days!
Ignore any crap about negative sleep associations or rod for your own back. Right now if the sling comforts them and gets you some rest? Do it. I slept upright with her in sling, one arm hanging out for safety at one point. She now sleeps on bed independently (although we co sleep). On those long rocking sessions, read Dr Sears Attachment Parenting: he'll make you feel really good about holding your baby (and give you some good, well researched comebacks to stupid HV who insist on you teaching them to sleep independently)
That said, rest is important. If someone else can hold them or they'll go in a rocker while you shower etc. do it. They'll possibly cry a little but its ok. You're an important resource.
Comfort foods I inhaled on strict diet? Colin the caterpillars and flapjacks full of dried fruit etc. I also ate junk food for the first time ever.