Yes it is possible. We did it for the first time with our sons the same age last year. 3 things I would advise.
1: As other have said you can't do it all in 7 days so don't try. This doesn't mean you can't do a lot but don't expect to do everything at all the parks, eat at 7 different resorts and hit all the shops in Downtown Disney and still be relaxed. Just not possible.
2: Have some sort of plan as to what you want to do and when you would like to do it. Many folk will advise just waking up and doing what every you feel like but with kids that age you should have some idea of what you want to do. In particular make ADR's for the popular places if you want to go there and have an idea about what counter places you would or would not like to go to. (For example in the WS I think the American Pavillion is the only CS place with Air Conditioning. In August that made the decision for us.).
3: Accept that you may have to chuck the plan out the window 5 minutes into a day. While having a plan helps don't become driven by the plan. For us it was the realization that our 6 year old son wasn't going to go on any dark ride that was the least bit scary. We went from riding POTC, HM and such to riding Peter Pan more times that I care to think about.
One other thing I would reccomend is taking a look at Tour Guide Mike. We used it and one thing that he emphasises is how to have a relaxing resort experience. We used his advice for our 7 night trip with our sons 6 & 8 at the time and saw quite a bit but also did have the relaxing resort vacation experience he talks about.
Good luck with your trip.
Edited to add: One other thought. Keep your expectations of the "Magic" in check. Sometimes people expect too much from WDW and no matter what they get disappointed and then upset and there goes the relaxing vacation. Don't sweat it if things don't go the way you expect them to.
1: As other have said you can't do it all in 7 days so don't try. This doesn't mean you can't do a lot but don't expect to do everything at all the parks, eat at 7 different resorts and hit all the shops in Downtown Disney and still be relaxed. Just not possible.
2: Have some sort of plan as to what you want to do and when you would like to do it. Many folk will advise just waking up and doing what every you feel like but with kids that age you should have some idea of what you want to do. In particular make ADR's for the popular places if you want to go there and have an idea about what counter places you would or would not like to go to. (For example in the WS I think the American Pavillion is the only CS place with Air Conditioning. In August that made the decision for us.).
3: Accept that you may have to chuck the plan out the window 5 minutes into a day. While having a plan helps don't become driven by the plan. For us it was the realization that our 6 year old son wasn't going to go on any dark ride that was the least bit scary. We went from riding POTC, HM and such to riding Peter Pan more times that I care to think about.
One other thing I would reccomend is taking a look at Tour Guide Mike. We used it and one thing that he emphasises is how to have a relaxing resort experience. We used his advice for our 7 night trip with our sons 6 & 8 at the time and saw quite a bit but also did have the relaxing resort vacation experience he talks about.
Good luck with your trip.
Edited to add: One other thought. Keep your expectations of the "Magic" in check. Sometimes people expect too much from WDW and no matter what they get disappointed and then upset and there goes the relaxing vacation. Don't sweat it if things don't go the way you expect them to.