Couldn't agree more with junebirthdaygirl.
What the OP has here are three teenagers, behaving unpleasantly as teenagers often do. It is a cliche that children go through a selfish, rejecting stage towards their parents in their teenage years - often being very rude and offensive - before emerging from the chrysalis to become delightful adults. It would be terrible to reject these three young people, who have already suffered abandonment from their father, at this vulnerable and crtical age. That is not at all to say that the OP should tolerate some of their behaviour - the insults must stop and there must be rules about helping out in the house. But the idea of ceasing to love them, or throwing them out to fend for themselves, is horrendous.
The reason the OP is having such a terrible time with her teenagers is that she has three and they are ganging up on her. One rude, unco-operative teen can severely affect family life but three must seem like a nightmare - a united , hostile front, ranged against her. Each one is probably not worse than many teenagers, but with three in the house, the OP has become the outsider, trying in vain to impose her values and standards of behaviour on what has actually become a dominant group with its own, different values and views. And the OP is on her own - unsupported by a partner her own age, who could help her get things in perspective, and having her attempts to manage things sabotaged by her ex. I have the utmost sympathy for the OP.
My advice to the OP is to firstly echo what previous posters have said about tackling the boy one by one -explaining how unacceptable their present behaviour is, and how it must change. Mention particular incidents and discuss them calmly, looking for common ground. Do not avoid expressing your sadness and sense of isolation caused by their behaviour - address them both as the head of the household and as an individual. I would be amazed if this did not make a difference - it is much easier to see someone else's point of view if appealed to as an individual, rather than as part of a pack. Try to contine to have individual relationships with each of them. Then, as everyone has said, cut down on the amount you do for them and let them do their fair share in the house. Do it calmly, gradually and not vindictively - what you are aiming to establish is fairnss, not revenge. So, for example, buy the ingredients for dinner, let them know they are there and then leave them to it. Show them how to use the washing machine, where to hang up the wet clothes and let them get on with it. Not only will this leave you feeling much less resentful, - at giving so much and getting nothing back in return - but it will increase their respect for you as they see how important a contribution you have been making to their lives. They will not manage the cooking or laundry nearly as well as you and it will do them good to lose their present sense of superiority! You have lost your childrens respect by being too accommodating - this is the time to claim it back.
I honestly think that these measures would start to right the balance of power in your family and begin to improve your relationship. The key is determination and consistency. When they see that you have really changed - in your expectations and self-respect - they will change too.
Most of all, realise that all this will change - you are just at the nadir at the moment. If ever there was a time for the MN mantra "This too will pass", this is it. Young brains develop, personalities mature and obnoxious teenagers often become charming young men in their twenties. As a previous poster said, your sons will realise, as adults, all that you have done for them and love you for it. They will see and appreciate the difference between how you have treated them, and their father. Parenting is a long game - don't give up, OP!