I have a 3 1/2 yr old and a now 9 wk old. I found when I sat down to feed DS or try to get him to sleep DD would start with "I'm huuungry". Not sure if your kids will be up for it but we went shopping for a lunch box (make sure they can open it themselves!) and now we pack a lunch for her. I put stuff in there I am happy for her to have and she can get it out any time she likes. I just don't have any control over what she eats when so sometimes I only put a treat in there later when she has had most of the good stuff!
I also find that DD copes better on the days we get out of the house. Maybe see if there are some groups in your area (we go to tiny tots at the pcyc) or it sounds like a fenced park would be ideal. Then I pop bub in a sling and he is out of the way and I can still push the swings or things.
I'm sure you will find ways of doing things that work for your family!
The lunch box idea is a good one and also get one for yourself and pack it each day and a drink bottle so then you know that you have something to grab at any time.
Make some meals that you can put in the freezer- even frozen mince with veges or tomato sauce in a bag is good because then all you have to do is cook pasta. I would cook double meals on my good days and put them in the freezer to replenish my supply.
You will find that a 3rd baby will slot into the household. Wash the baby with the other kids and then wrap baby in a towel and put on the ground in a safe place or bouncer while you finish washing the others.
You can prepare brekkie at night for the kids eg put the cereal in a bowl and cover ready to just put milk in them you have 1 minute spare to feed the baby at the same time. You can pack the lunches then too.
I also think though it is hard to get out if you can even walk to the park during the morning sleep-time so the other children get to burn off some energy. that way you can come home have lunch, put the 2yr old to bed for a sleep, chuck a DVD on for the 31/2 yr old and get comfy and feed bub. You may even get a bit of time to breathe if you are lucky.
Invest in a good baby sling so that you can wear your baby while you are doing the things that you need to do for the day. Include the kids in the baby play time and encourage them to interact... but use prompts like, ' I'm going to put .... on the ground for a play now are you going to join in? Where are you going to sit? What toys shall we get? Remember to be very gentle, thats great boys 'etc
Good luck you will find a rhythm that suits your family, you will be great
smile