Right around the arena? I don't think there are any hotels with open indoor pools around there. The Hyatt Regency at 400 New Jersey Ave NW on Capitol Hill, a few blocks from Union Station, has an indoor pool that appears to be open, although you should check directly first; or the Homewood Suites by Hilton close to the Navy Yard Metro station might be an option as well. Personally, I'd recommend looking around the Navy Yard area for restaurants that may catch your interest since the area has certainly changed since you were last here. The area directly around Union Station, besides Union Station itself, is pretty sparse for family-friendly options although I'm pretty sure they let kids into the Dubliner.
That being said, Metro is a bit of a mess these days, with longer times between trains on all lines due to problems they've discovered with the 7000 series cars.