Well, my children aged 20 and 22 still squabble over some things.

It is common for children of that age to fight over everything. Even buying them identical toys will only help but so much because when either one loses a toy or breaks it they will claim the one that is not lost or broken is his/hers. I do not have kids who are in their 20's but I do have four young kids, and I am 20something myself with 3 brothers close in age. I can tell you that we fought all the time and would get along like 30 minutes later all the way up until we were all pretty much grown. Its just a part of being a parent so good luck!!

I can definitely relate! I have a 2 and 3 year old and they went through that, and still do, to a degree. I know that we are very busy people with a lot of things to do and it's really difficult to do what I'm going to suggest, but I tried it and really saw a drastic improvement. I used to just let them kind of settle it themselves or do the whole distraction thing, substitute it with something else for whichever child seemed less insistent, but then I really tried being involved with their playing, being on their level and actually being part of it and would constantly interject, acknowledging nice behavior and taking turns, and also pointing out when something was 'not nice' or whatever else. it sounds so cliche and I completely understand that and don't want to sound all suzy homemaker on you, especially if your children have outside childcare, which makes things SO much harder. Anyway, maybe you can modify that and try to make it fit your household's lifestyle, but it really did help and now I will even hear them say to each other (sometimes) "oh, that was so nice" or some other business like that, but that's just my two cents :-)

You need to sit them down and explain that they shouldn't interact that way. If my children fight I tell them they can't play with one another until they are nice and treat them how they want to be treated. In about 2 minutes they decide to be nice. Fighting is a way for them to test eachother's limits and bonding. Find a game like hide and seek or one that they take turns in to teach them turns. They may need more one on one attention from you or daddy too.

Sibling rivalry. Short of keeping them in separate rooms, there's nothing else you can do but let it take its natural course till they grow out of it, kill each other, kill you or kill one of them or both

Well . . . according to tv, every time they do it, you have to put each of them on the "naughty rug" for the number of minutes equal to their age. Every time. Soon they will stop. You have to persist without exception.