Splintering deck - correct process?

We have a very large deck area around our pool that is in bad shape. We REALLY need some help figuring out the best process to make the deck safe again for people to walk on.

The previous home-owners had the deck entirely covered with green outdoor turf, probably because of splintering. We removed the turf b/c it was falling apart (and not good for the deck) but now it is dangerous to walk on.

It is bowing considerably in several sections, but nothing is rotting. I know we will need to replace several of the boards b/c they are splintering/cracking too badly. We can't flip the all the boards b/c they are each nailed down in so many places and the nails are very rusty.

I believe you do not generally recommend sanding for decks? However, because our wood is splintering and has lots of cracks, I think this is the only option we have to get rid of the splintering.

Could you help me with the order - this is what we were thinking:
1. Replace bad boards, tap down nails, remove staples
2. Sand deck
3. lightly pressure wash to get rid of dust. Let dry
4. put on a sealant to protect deck

I'm trying to figure out if/when we would clean in this process. I'm hesitant to use a cleaner b/c I can't wash it off toward the pool and we have a garden next to the deck on the outside, so I don't want to wash it off into the garden. If we sand and then lightly power wash to get rid of dust, would that be sufficient? We aren't going for cosmetic at this point, just safety.

Any help would be greatly appreciated!!! Thank you!