First off, congrats to your daughter racing in the nationals and good luck to her!
Is she racing the whole time? Mahone Bay to Dartmouth is a bit of a haul, also kind of a pain traffic wise. If you are coming into town in the morning give yourself lots of time because it will likely be slow at rush hour, although not as bad in the summer. It's also a bit more complicated coming from that direction. Make sure you get off the highway in Halifax and then go across the bridge to Dartmouth, you don't want to end up going around the basin. Either bridge will get you there, personally I'd take the MacKay if traffic's heavy as it's pretty well all highway; the MacDonald is a more direct route but also involves smaller roads and is a bit more complicated. The bridges cost .75 per trip - cash only so make sure you have some before you get on it (toll is on the Dartmouth side). BTW if locals are talking about the bridges they do not call them by name - the MacKay bridge is called "the new bridge", the MacDonald Bridge is called "the old bridge"
Hopefully you won't be going in every day on that first week, as it is quite a distance and gas is expensive in NS. Get the most fuel efficient car you can.
Chezzetcook is not so bad, still a good distance but more direct. Just take the 107 all the way into Dartmouth, then exit onto Prince Albert Road. The lake is right there.
I don't know where you'll park, it will be a busy spot.
If you are at the lake on the first day, there is a big Superstore right up at the interchange where Prince Albert meets Braemar. If you are going right to Mahone Bay there is a Sobeys on one of the exits off the 103, I believe it's the exit to Hubbards but not completely sure. If you are looking you can see it from the highway. I don't know if there is a big store in Mahone Bay, but if not there are all the major stores in Bridgewater (Sobeys, Superstore, Walmart, Zellers, etc).
Mahone Bay is absolutely beautiful, lots of little shops and such. You'll want to take an afternoon or evening to just stroll along the waterfront and windowshop. You should also go down the waterfront in Halifax. I would park in Dartmouth, since you are there anyway, and take the ferry across. There is a walkway all along the harbour, just don't look in the water
As far as other things to do and see, it depends on how much time you have between races and what you are interested in.