Within 3 hours of Calgary and a lake ... not a whole heck of a lot. Not a well published fact, but "Calgary" is an old Cree word for "not a whole lot of water within 3 hours of there", and not, as some claim, as some Scottish word or some such nonsense.
Seriously, for lakes, that's pretty slim pickings. You're looking at Kananaskis, Minnewanka (holy crap cold), Waterton (holy CRAP cold), Little Bow, Sylvan, Aspen Beach, Old Man, .. um.. Lake Newell ...
Well .. actually, see the thing is, if you say "within 3 hours of Calgary" .. Edmonton is just on the edge of that kind of distance, and there are lot of lakes up that way. But if you're looking for something "comfortably within" 3 hours I'd look up those I just listed (with the exception of Banff and Waterton, all are provincial parks).
I'll plug one in particular - Aspen Beach provincial park - it's on Gull Lake and about 2.5 hours north of here. About 20 minutes north of Sylvan Lake. Sylvan Lake is a nightmare on long weekends, I'd forget going there. But Aspen Beach - wow is it ever nice. I'd camp there in a heartbeat if it wasn't for the fact that my inlaws have a place on that lake. I just spent the last week up there, taking my 2 year old to the beach. If you have little ones, they'll love it. The lake is very shallow (21 feet at the deepest point) so it's warm, but it's remarkably clean for a prairie lake. Aspen Beach is on the south end, which is the shallow end ... you can walk out seriously like 100m before you get to waist deep - so again, very good for little kids as there's less worry about them getting in over their heads so-to-speak.
I can think of about .. hmmm easily about a half-dozen provincial parks within the area with lakes, but not really "beach" spots. Old Man is not bad, but it's sort of a ... well ... if you're not into windsurfing or kite boarding it probably doesn't have a darn thing for you. It's just a body of water with a LOT of wind (seriously, it's kind of worth seeing if you're into windsports - but - kids will probably be bored to tears).
Really it comes down to Aspen Beach or Sylvan for good beach spots. Oh no wait, Little Bow has a nice beach or two, never mind me. But I guess what I'm getting at, Sylvan is too close to Calgary and Red Deer to be a practical long weekend spot. Plus it's full of rowdies on a long weekend.
Aspen Beach on the other hand - only 20 minutes further (so you could go down to Sylvan for the day if you wanted - it IS a nice long beach worth seeing - the beach is, in fact, in the town itself and is a "day use only" provincial park so you'd have to camp in the .. hmm I forget the name now -- but it's about 5 minutes drive from the beach). Ack, I keep digressing from my main point. Aspen Beach is a "dry" park on long weekends - ie, they put in place a liquor ban for long weekends - sort of a drag if you like the occasional beer or Smirnoff Ice or something - but it really drives the rowdies away, making it an ideal family spot.
Anyhow, there's my recommendation: Aspen Beach. I hope you can get it, check to see if you can make a reservation maybe.