A few points that might be useful as you get started. The chair is nothing more than an old chair needing a little TLC and refurbishment so I wouldn't get overly hung-up about A-Z refinishing it so that it looks like a brand new heirloom to be.
1. Sand a bit more with 80, 100, 120 grit if you wish but don't stress over it-you'll never get all of the nooks and crannies. A rocking chair has almost zero flat spots for sanding/scraping, etc.
2. Sand/prep the underside of the seat like you've done to the visible parts topside. Try a few coats of your oil finish on a portion of the seat bottom and see how it looks and feels to you and your wife.
3.
Leave them alone entirely.
BTW, Formy's Tung Oil Finish and Watco Danish Oil Finish are marketing terms that have little to do with what is actually in them. They're both made to look like a true tung oil finish while most don't contain tung oil per se.
Here are few of the real deal products for your information:
https://www.waterlox.com
https://www.realmilkpaint.com/shop/oils/pure-tung-chinawood/