Lots of applicants are taking rigorous courses and have very high grades so you would probably need to explain that well. SSAT is basically a benchmark, so it would help if you had a good score. Good recommendations would also help a lot.
I don’t think doing the summer program for any school would increase your chances that much. If you really want to go to boarding school, I recommend casting a wider net unless you have a good local option to fall back on. ECs look nice so based on what you’ve shared I’d say your daughter has a good chance.