Any of the RI in DC itself are really good! Their amenities, location and prices are about as good as it is going to get!
Some of our MRI folks actually live there and really know the city well! Personally, when traveling with a few people, I have found the JW to be just wonderful. The CL Lounge affords a fantastic view of this historic city!
Fortune is smiling on you for your upcoming visit, due to the heat and the summer doldrums when less business is conducted, hotel rates are attractive relative to their normal charges, in August. Here are some thoughts;
With family wanting a pool and near a mall, my first choice would be the Pentagon City Residence Inn - still a Cat. 4, so if you have certificates you can use them as well. Terrific Thursday thru weekend rates starting at $89 make this a great pick (meaning, if necessary, I would look at two separate reservations, if the prices vary that much - 4 day great rate, 3 day normal vs. 7 day which can sometimes forget all about the 4 day figures and hit you hard, and as you no doubt know, with low occupancy, which is why the rates are low to begin with, they seldom make you change rooms - especially platinums). Free airport shuttle, easy Metro transportation into the city, two blocks to Pentagon City mall (where a Ritz is an anchor to give you the vibe of the mall) and shops and restaurants around the mall as well. Granted a modest indoor pool, but it will give the kids some water time.
The two Crystal City Marriott's are fine also with similar features (and the Gateway has an indoor/outdoor pool).
The Residence Inn near the National Mall is also nice but priced $100 more per night probably due to volume, so I would use the money elsewhere on your trip.
Downtown - the JW is as jerrycoin says very nice, but I don't think they have a pool. The Mayflower similarly (a bit further uptown) is a marvelous property with great summer weekend (as in four days) rates, but no pool. I like the Marriott at Metro Center, but it's not near your requested mall (as in shopping - it is walking distance to the National Mall - Smithsonians, Capitol Building, etc).
On the western part of town across the river from Georgetown is the Key Bridge Marriott, which has nice views and an actual outdoor pool (which also gives you an indication of the property's age) but could present transportation issues for a family (but it is close to the Rosslyn Metro station which takes you into the sights).
So take a look and welcome to town. Don't forget to check out possible activities deals on NL East Rivals Battle as Mets Meet Nationals | Goldstar
and if you're still in Bethesda (one of my favorite properties) be sure to walk down Elm to Woodmont and check out Bethesda - Jaleo if you haven't already, very nice meals (American Tap across the street is a pleasant stop for sandwiches and a brew or two).
Enjoy your visit.
If it's your first (and only) time to DC, I wouldn't recommend it, but we like the Westfields, which is out near Dulles Airport - and, I admit, I've taken the kids there during the winter when there is good weekend rates just to hang out in the indoor pool and enjoy a terrific Sunday brunch - also, a very good (well managed) golf course - but it's a llllooooonnnnngggg ride into DC from there (and it's not METRO accessible) - Chantilly Hotels | Marriott Westfields Washington Dulles Hotels
Some additional threads to consider for your DC trip: