I am really sorry that you are having issues. I don't have any great advice, just wanted to say I am having the same problem too (although I only have the one). DD and my nephew (whom I looked after in the school holidays) rang rings around me and I felt like I couldn't even take them to the supermarket without it turning into a massive disaster.
What I'm doing at the moment with DD is really cracking down on absolutely everything. Ignoring her made no difference, if anything it made things worse as she did more and more to get my attention. I tried praising every single good thing and set up a star chart system with very mixed results. So now all back chat, throwing things, yelling at me, naughty behaviour, or just not doing as she is told gets "thinking time". Basically I don't yell I just send her straight to her room. She's allowed to come out whenever she wants but only if she behaves nicely. It takes a lot of effort to be consistent but it is slowly working. I explained to her that if she couldnt behave she would spend a lot of time sitting in her room, and then started sending her there. I have noticed that she backchats a lot and will argue the point till she is blue in the face and now I don't get drawn in. I make a decision - for example tonight it was eat your dinner or leave it alone (no playing with food) - then follow through every single time. So tonight she got a warning (eat your dinner or don't but stop playing with it or you will go into thinking time). She started to argue so I repeated myself and she started yelling its not fair (and other stuff) so I went right go to thinking time in your room. Usually she either falls asleep or comes out and says sorry.
The theory is that they get the idea they can't join in with normal family life until they can do as they are told or behave. I don't get as stressed coz I have a consequence already thought out and I don't get drawn in to arguements with her. She will happily go to her room (she plays with her toys) but knows that to come back out she has to do as I say.
Its not something that works when you are under time pressure, I have yet to solve that problem (we have a lot of issues with breakfast, teeth brushing and getting ready in the morning for daycare). But it does seem to work really well for other stuff at home plus it keeps my stress levels down and leaves me calmer to be able to deal with the problem.
I hope you find something that works for you. Its really hard when they behave badly - I felt like my bloodpressure went through the roof when I had both my DD and my 5 year old nephew behaving like that.