Not inside the National Park, but the Fundy Trail Parkway is a lovely drive originating in and returning to St. Martins for great views and exhibits.
Inside the park, the Headquarters Campground is closest to Alma, but it's a few miles. (Not a convenient walk for a quart of milk.) There is a beautiful covered bridge, numerous hiking trails. Kayaking. IIRC, there is a swimming pool inside the NP, though we did not use it.
Close by is the Cape Enrage Lighthouse, which is scenic and also has a zip line, if your daughter could handle that.
You'll find that it's easy to schedule your visit to Hopewell Rocks to see the "flower pots" because there are numerous brochures with the summer tide tables in print. Online, too. I found the Rocks to be a fun attraction, and it's a well-run operation. It's a pleasant walk to reach them, and a staircase down to the sea floor...on the way back, if you are tired, you can board a tram at the top of the staircase for a ride back to the visitor center for a modest fee.
If I were visiting te area again, I'd stay in the park, but move to Ponderosa as mentioned above for a night or two, to see the Rocks.