Rubyred - your thread really struck a chord with me when I read it last thing last night, and I went to sleep thinking about you.
So I've got loads of thoughts, and hope something is of some help to you. Btw I have two boys are 4.5 and 6.5.
I'm sure you are a great parent - I've always found things are better 'out of the house', and that doesn't have to be a bad thing, or a bad reflection on you or your children. If you can isolate 'flash points/bad times', see if you can arrange to go out at that time. Try and arrange several little outings over the weekend to break things up a bit. Until very recently I HAD to get the boys out of the house whatever the weather and have some fresh air before 9.30 am every day (bit like walking the dog), otherwise all hell broke loose. So we had little routines like going to fetch the paper on a Saturday. We also have swimming lessons first thing (8.30 am - ouch!) on a Sunday. I find that after a little trip, they will quite often come home and play together nicely for a while.
Try not to have too high expectations of them - they are still very young, and co-operating socially is a difficult skill. Try and identify individual activities that they can do to have some space from one another. My boys are older than yours, but still over the holidays they spent more time in separate activities than in joint ones. (Reading a book, playing on the computer, drawing or doing some craft activity, building with the Lego.)
When you do think they are in a good frame of mind to play co-operatively, give them a specific suggestion, and a promise of a reward after a set (short) length of time - say 30 minutes if they have coped OK without squabbling.
A lot of this is completely normal, and just kids growing up. I always have very low expectations of them in the hour before bedtime, when they are exhausted. But I was surprised to hear you relate stories of them arguing first thing in the morning. Maybe the 'breakfast bowl' type of arguments have arisen because they are so close in age. You may have some success by being super-strict about such things for a brief period. "I give you the bowl with the breakfast in it ... no complaints. If you argue about it, you get nothing." ... And of course loads and loads of positive rewards for good behaviour.
In this house we have zero tolerance of violent/aggressive behaviour. I don't believe that boys have to constantly hit and kick one another. They don't accept that sort of behaviour at school, and I won't tolerate it in my house.
Sorry this is so long - hope some of it is helpful to you. Feel free to ignore the bits you don't agree with!
Just felt I should offer my point of view. My boys are not angels, far from it, but constant squabbling and fighting is very wearing to witness, and is not doing anyone any good. I don't think it's necessary, and I do think - unlike lilibet - that things can improve, it doesn't have to stay that way.
Good luck - do let us know how things go.