Just FYI, ALL the "beaches" at the Disney Resorts are no swimming-didnt know if you knew that. So, basically, the beach time with my young ones wore off it's novelty within a couple of hours, so the rest of the time was spent at the pool.
If you're planning on going back to your resort in the afternoons for naps or for meals or whatever, unless you're staying at a Monorail resort (CR, Poly or GF) or Beach Club/Boardwalk, and you're relying on Disney transportation, this will take at least an hours travelling time.
I've travelled with my boys since birth (sorry I am clearly addicted) and have stayed at almost every Disney resort, so I am offering my advice from a well seasoned WDW traveler and mother of 2-perspective.
If I were going to pick a moderate resort that is convenient and has a nice pool for the kids, I would probably pick POFQ (Port Orleans French Quarter). But honestly, I would go to a value with kids of your age. The biggest difference between the values and mod's are the grounds and size of room (which is only slightly bigger in a mod vs a value) and slide.
If I were you, I'd pick a value and spend the extra (50% cost btw) and rent a car. That way you could travel quicker, go to the resort for rests and explore more of WDW spending less with still great accommodations.
The kids will LOVE the theming at the values as well. We only travel value or Deluxe, have completely cut out the mod's; just not worth the extra expense for us.
NOW if you want a great pool and activities for the kids (caution...lots of money involved) the best pool by far in WDW is at Beach Club. We stay there and spend at least 3 full days at the pool alone. However, this will cost you twice as much as a moderate and 3X as much as a value...
The first trip to WDW can be incredibly overwhelming and stressful. Remember, at the end of the day, you're at WDW..ENJOY wherever you are!
Just my opinions. If I can help in any other way with WDW info. or as a mother of 2...just let me know.