You just don't get the point, do you? You started a thread and we thought you were genuinely asking for advice. Perhaps you were and all who think you are making a rod for your own back have missed the point.
You want to go on holiday without your DSs. Why? What sort of holiday are you wanting to take which doesn't involve your family? Don't you think that having produced a family, you are responsible for them?
Perhaps you can live with yourself if anything happens to them while you are away? You say their father lives nearby. You divorced him and have custody of the children: now you are happy to leave them and expect the father you divorced to care for them? Are you sure he can? Are you sure he wants to? Are you making him responsible if your house trashed and your boys gone. because other teens discovered you had left your house unattended and your children alone and vulnerable?
You may be confident about your DSs ability to cope: are they confident? You give them no choice. What you are saying to them, as well, is that they should learn to defend themselves if intruders break in. Why should they?
THEY ARE MINORS. You are in loco parentis. That means while they live with you you are responsible for their safety. Even if you leave them to come home after school to an empty house, you are responsible. If something happens to them, and the house, you have mitigating reasons which might help you, but you are still responsible.
How much more if you leave them alone for a week?
You want us all to agree and say 'go away on your own for a week. What a splendid idea, and we hope you have a fantastic holiday', but we won't all do that, because we would never leave our minor children exposed to danger.