Agree with others that IMO she's best unshod unless necessary, & I don't see how shoes would be necessary/helpful for this. Sounds like she may need protection for the face of the wall, but there's no reason to put anything on the ground surface.
The 'split' was an abscess that burst at the coronet, either due to a trauma(she bashed it or such) or possibly a laminitic episode(tho if it's just one small area, I'd say more likely the former). If the split were near ground level, especially if her walls were overlong at all, it may be purely that the horn below it was just under too much mechanical force, so broke off. Unfortunately, splits & such often go hand in hand with infection, which can eat away at surrounding tissue & weaken it, which is another possible reason for the breakage, which I think is more likely if it was still only half way down the capsule(which is a term for the outside/horn, not inside).
So I'd treat any infection, but if it's close/in live tissue, be careful of using too strong chemicals which can also cause tissue damage. If there is a substantial amount of wall missing that has left the inner foot exposed, then I would consider booting or such when riding, to protect her in case of kicking rocks or anything(or punctures). If she's kept in a regular pasture setup, then she may be fine without protection when at home, but you'll have to consider the rocky creek crossing & likelihood of stone bruises(far more likely than punctures IME). You might consider just a bell boot or such for a bit of added protection, as booting 24/7 is not generally a good move and you don't want to seal the area from the air because infection tends to thrive in anaerobic environments. If possible, I'd probably fence off the creek & give her water from a bucket for the next month or so if worried.
I wouldn't personally bother with 'hardeners' or other topicals. Hardeners often include formaldehyde which IMO doesn't belong anywhere near hooves... well, live ones at least. Hardening makes hooves brittle - therefore more likely to chip & split because they lose their plasticity. Chemicals such as formaldehyde also kill live tissue, so if there is any exposed or close to the surface it could be damaged. Other topicals, such as oil based 'moisturisers' are also not great for hooves IMO and in this situation would potentially just seal in any infection & make it worse.