Local to NS here. I think what provinces you hit strongly depend on your interests. Are you more into museums? Outdoor experiences? Cities?
We're small, but we're not *that* small. You could easily spend most of your 9 days just on driving (and I assume you're renting a car? You're gonna want a car.). For example, Halifax to Sydney is around 4.5 hours of driving with one quick stop. In the other direction, Halifax to Yarmouth is around 3-3.5 hours.
Unless there's something absolutely amazing in NB you are dying to see, I'd skip that province (Sorry New Brunswickers, you've got a rep and you know it lol). Anything you can experience with the Bay of Fundy on the NB side can also be easily experienced on the NS side.
Depending on your travel plans, I'd highly recommend stopping in to one of the villages in NS - Acadian village, Highland Village, Sherbrooke village. They have renactors in costume to tell you about the time period you're "visiting". Lots of fun! Other similar experiences can be found at the Halifax Citadel and Fortress of Louisbourg. If you do go to Louisbourg you can easily allot a whole day just to wandering around and catching some of the interpretation activities. Another shoutout to Glace Bay where you can visit an actual coal mine.
I think you would want to pick a direction then maximize your time in it - for example, either go west from Halifax and around the South Shore/Annapolis Valley (you could in theory hop over to NB from here on the ferry. It's not that cheap, and depends how badly you want to explore NB). OR go east to CB, explore either the Cabot trail area or Sydney/Louisbourg/Glace Bay (you don't really have time for both unless you want to just hit the highlights), then loop back and take the ferry to PEI. Spend 2-3 days on PEI then take the bridge back to Halifax. If you choose the south shore/NB option, you could reverse direction on getting to PEI - take the bridge over, and the ferry back. I do recommend the ferry - it's fun to get some ice cream on board!
Any questions just ask