I feel your pain
I know what it is to look at other people's children and know that your kids present you with challenges that the other parent is not facing. And then it is even worse to hear that parent tell you that she used the standard method and it works fine (and perhaps you are just doing it wrong). I went through the same issues with sleep with my DS. So I know that sometimes it is the child who is different and the parent is doing her best!
With that said, perhaps I can offer some additional ideas?
The first is to remember that even if you don't get anything cleaned, or cooked, or household projects done, you are still doing a full-time job each day. People who work often hire full-time nannies who are there to provide childcare only to children (especially to 3 young children!). Are your children loved and nurtured? Yes. Then you have completed a full job.
However, it sounds like you would like to get more than one job done each day

. So one idea is to involve your kids with you in the job. If you want to sweep the floor, get out four brooms so everyone gets one. Then resign yourself to spending an hour doing a job that should take 10 minutes. Turn on the music, trade brooms often, and have fun. Be prepared with a wet cloth to quickly wipe up and discard any actual piles of dirt that you can put together - or they will be soon scattered again!
Another idea (new for me, but it really does work) is to clean up as you go. I find with my 3.5 year old that when we finish a meal, I can say to him "Please put your dishes on the counter. Then when you're done with that, we can play." It takes him a while to get them to the counter, and during that time, I clean up the rest of the meal. Your older kids are old enough for this, and perhaps for your younger child, you could tell him that he needs to remain in his high chair until the meal has been cleaned up (perhaps have a special toy reserved just for this time?). Or perhaps your 4 year old could be responsible for his dishes, and your oldest could be tasked with both taking care of her dishes, wiping the baby's face, and taking him to the family room and singing him a song? When I implemented this idea ("I'll be able to play with you after you do _____"), it took a couple of rounds of my DS getting upset and me sticking to my rule before he understood the concept and was ok with it. I'm sure you will be loving and gentle as you remind them. Sometimes my DS would go and do something else before he cleared his dishes. There was no hurry, he wasn't in trouble, it was just that I wouldn't be able to pay attention to him until his dishes were cleared (except for the loving reminder). If he did something "naughty" to try to get attention during that time, I would give him a hug and say "it looks like you really want some attention. Let me keep you company while you clear your dishes, and then we'll be able to play together."
Lastly, how do you feel about TV? My DS gets two "Television Times" each day, and each lasts for 30 minutes. One is after breakfast (including cleared dishes) and one is around 6:00 so I can prepare dinner. I find I can be very efficient during this time. Oh - and I have a rule that he must complete his "Three Things" before I turn the TV on. I look around the house and select 3 tasks that he must do. Usually they are things like "put your toy cars into their bin", or "come with me to get the mail". There have been times when he chooses no TV instead of doing the Three Things (ugh!), so I let him pick his show first so he is excited about it. With 3 kids you could have 4 or 5 things and have them all work together to get them done.
Best of luck with all this!