Also...you are definitely not alone, my kids can be very hard too at times.
"They often fight with each other." So do mine and it's crap but one thing you can is separate them.
"I work full time but never get to go out to an excercise class or socialize." I'm sorry this must be very hard. Can you invite friends over for a take away night? Get exercise DVDs at home (I know it is not the same thing but any exercise if good).
"Unless I'm constantly on it with on tap activity and entertainment, they just want to watch shitty YouTube clips of loud..." Let them.
Really allow a certain amount of mindless fun per day, you are knocking yourself out and you don't need to ban all Minecraft games /Peppa pig, BUT they must use earphones when they wake up or cut the wifi.
'They don't respect my authority and constantly test my boundaries.' I would personally try and make some simple rules and stick to them. Maybe have some families meetings and chat (pass something around, a toy trick or whatever works (whoever has the truck talks), get their views but make sure it ends positively. Making things better for all three of you. Have some treats that you can afford (the odd take away, trip swimming, chocs or whatever, movie night with popcorn at home works well sometimes). Offer the rewards when you get the behaviour you want.
"They refuse to get ready for school on time in the week. I have to dress them both like babies."
Don't dress them, start earlier and leave earlier than you normally do. When they can dress themsevles with miniamla fuss earlier reward with a bit of 'quiet' early morning TV or whatever.
" I feel like going to get ill at this rate. They moan and tantrum if they don't want to do something or as soon as I turn off the tech." I think you may get ill but don't expect that to move them, they are too young to understand all you do for them. I personally think you need to make life better when they behave (praise all good efforts from them, don't shame them for needing help to dress but praise them for getting ready on time).
And if you have tried all this and it has not worked then maybe someone else will have some good ideas.