Not knowing you or your children I will give this my best shot: You and your kids need a break from eachother & the kids need a break from eachother too. Also you need to be much tougher on the 2 older children. Tougher meaning you have a time out area, mine is a wall where there is nothing they can touch or play with. THE MOMENT they act up, whether it's mouthing off, talking back, fighting, teasing, acting wild etc, they go there immediately. Do not let them get up for any reason at all. This obviously will take time & lots of it but you MUST be extremely consistent.
As for your daughter who you beleive has ADHD, well pursue that with her Dr, the school social worker, her teacher (if she is in school), there is a test so do that ASAP.
I don't believe your long distance family situation is the problem. We don't have any family & my kids (6, 5, 3) don't have much of a bond or relationship with their grandparents, they see them maybe once a month & they are not hands on at all. I think the biggest problem is you are probably burnt out from parenting & the kids can tell. I too get tired of the parenting by myself as my husband is rarely around, in fact we haven't seen him in 5 weeks & it's just me & the kids all day everyday. HOWEVER I am very strict & my kids act out but I am on them like white on rice. My middle daughter just turned 5 & she is & always has been a handful for me, our personalities clash big time, she pushes my buttons every minute of the day.
Some things to try are: get stricter, have some structured plans for them, let them help you more, and remind them that it's important to treat family kindly so they should be nice & want to take care of their family. Have them color, play a game, help make lunch, help put laundry away, help do dishes & unload the dishwasher. My kids don't get into as much mischief if I have them doing things that make them feel important.
Also remember that kids are individuals too. They each have their own personalities & you have to figure out how to relate to each of them. A website to refer to is www.difficultchild.com & I here the book is fantastic.
Hope I gave you some ideas & insight on what has been working for me.
And know that recognizing that your home is in chaos is the biggest 1st step so now take it to the next step & start implementing some of the techniques that we all have supplied to you. Best wishes.