In short, my US family and I have received confirmation that we qualify for the non-immigrant visa. Our plan is to stay 6 months with my Thai Father there.

My confusion is this - the US Visa application says, Non-Immigrant Visa: "Upon arrival, Immigration officer will grant a 90 day stay up to one year"

What does that mean? Will he decide on the spot whether we get 90 days or 1 year or somewhere in between?

A non-immigrant visa always gives you the right to stay for up to 90 days. You will be gettting a multiple non-immigrant visa, which is valid for 1 year. During that year you can travel an unlimited number of times to Thailand, but cannot stay longer than 90 days in a row. After 90 days you have to leave the country, but can come right back in the same day for a new 90 days.

So your half year stay means that you will need to make a border run after 90 days to get a new 90 days.

It also means that if you were staying long enough you can stay for up to 15 months by doing a border run just before the Visa expires.

The non immigrant O visa entry itself is 90 days. Only if it were a non immigrant O-A visa would one year be provided on entry.