Before I comment, there are more important questions I think. How long will your husband be working out of town? Is that by choice or necessity? I feel it is important that the children should be raised and loved by both parents -- in person. Why would a couple want to be separated from each other or the children? Moving would disrupt your 14 year old a lot to have to move away from school and friends if she is doing well in her current situation. Because of that, moving should be semi-permanent, not for short term reasons. As to renting, it is extremely risky. I know of countless stories, including my own, where the renters ruined their properties. You can check credit, references, income, etc., but there seem to be lots of people out there that could care less. Short term renters (1 year or less) may not care if you address all your home's issues as long as it doesn't affect them personally. You would want to put in the rental agmt that you do not intend to fix the pool or fence at this time. Anything you don't name, you may have to repair. Paying for a home repair warranty (like AHS) is helpful as you will only have to pay the first $50 of a covered repair. You guys would certainly need to get up to speed on how to screen renters, how not to discriminate, what your responsibilities are and are not, what their responsibilities are and are not, and how to make sure it is in a legal rental agreement.
Had your husband tried (or intend) to find a local job? If it is a great job that he hopes to keep, it has great potential, and the area would be good for you and the children, have you considered selling your house and moving there?