That really is a tough one.... What kind of distances are you shooting when you're at the pool? You'll want something with a low aperture (f stop) in order to get as much light as possible into the lens and have the fastest shutter speed (So the pics are nice and crisp).. There are lenses that will do that and double up as great birding/wildlife lenses but there's no point in evening mentioning them as they are over 2k.
I'd be looking at a Canon EF 70-200 F/4L. Now, it's a pro grade lens (With the L designation) but for the price it's a bargain. Absolutely fantastic IQ (Image quality), weather sealing, built like a tank.. You can pick these up used for around $500 (New $650). It's not the smallest lens, and it stands out. But at the of the day, who cares, you're worried about the pics, not whether or not people are thinking your wife is now a pro photographer
I wish you were closer, I could let you hand hold a bunch of the lenses I've got.. If there's a Henrys near you take your body in and try some lenses out.