Hi J.. I think Erin and the other Moms gave some really great advice. The only thing I'd like to add is this. If you can, try planning one day for each child to spend with just that child. I know this will not be easy with so much going on, but it will surely be worth it. Find someone to watch two while you take the third, and just go somewhere. It can be to the mall, the park, the skating rink, the mountains... somewhere that the child likes to be and would have fun with you. Spend that day talking with that child about anything and everything. Don't make the whole day about their problems, talk about other things too. I think you need to do this whole day thing (rather than just asking them at home) because when you do you are showing them that you care about them individually and are really tuned in to what they have to say. But at some point during the day, just ask that child point blank how he/she feels about your home life and what has been going on. Ask them what they think you can do to make things better, what they would like to see change in their siblings, and what they think THEY can do differently to make life better for them. I think this time will give the children a sense that you are plugged in and really care despite the limited amount of time an attention you are able to give them on a daily basis, and it will give them a sense of ownership in the problem. I know their individual emotional problems play a large roll in what is going on and those problems need to be addressed. But any child, no matter what emotional problems they have, wants to feel heard, understood and taken seriously. So do what you can, even for just that day, to make that child feel that way.
Then once you've gotten input from all three, sit them down together and talk about the plan you come up with to make some of the changes they have each said need to be made, and the new rules of the house. I really like the idea of the chart with blocks to mark off when each child breaks a rule, but I would suggest also having a chart with blocks to check off when they do something good like doing chores, taking care of animals, being kind to each other, being respectful to you, etc., with sometype of reward (extra time watching TV one night, choosing the meal for dinner one night, having a friend over, anything simple and preferable not related to money but still incentive for them). In other words, they need to be discouraged from bad behavior, but they also need to encouraged to show good behavior.
I also want to ask... where is the father in all of this? Has he offered to help at all? Perhaps he should be the one to take the two while you spend the day with one. That may be another large part of the problem if they do not have a strong father-figure helping to guide them. Even if he does not live in the same house, he still has a responsibility to help raise the children to be responsible, mature adults. That may be another conversation you need to plan on.
I would also like to suggest a couple of other resources. Dr. James Dobson's book "The New Strong-Willed Child" is an EXCELLENT parenting resource, whether your child is strong-willed or not. Also, check out "No Greater Joy Ministries" online at http://www.nogreaterjoy.org.
Good luck, and hang in there!