Given your transcription ([hinner vella oof]), it’s hard to pinpoint the exact wording.
It would probably help someone who is good with dialects and the history of the German language (which I’m not) to know where your dad’s family is from.
Janka suggests Hintern voll auf (buttocks full up), but firstly, that’s not a phrase I’ve ever heard and secondly, I assume the [v] in [vella] is pronounced as in van, whereas the [v] in voll is pronounced as in fun.
The first objection I’d be willing to dismiss, because that’s 300 years of language evolution we’re talking about, but the second still holds, I believe.
Maybe [vella] is more like the German word wollen (to want sth.) and would be the contemporary Swabian pronunciation, and Amish people »came from various parts of the southwest corner of the German-speaking region of Europe«, including Swabia.
It does not really match the modern Palatine pronunciation though, and Palatine seems to be the main source of the contemporary Amish language (Pennsylvania Dutch).
Also, the language has changed a lot over time: »When individuals from the Palatinate (Pfalz) region of Germany encounter Pennsylvania German speakers today, conversation is often possible to a limited degree.«
So it’s nothing I’d wager my lunch on.
That being said, there is a modern German phrase that uses the same idea, namely the butt and the direction of up, but it does not sound close to the pronunciation you provide:
Hoch mit dem Hintern! / Hintern hoch! ([Get your] Butt up!)
It means someone should overcome laziness or an initial hesitation when they should do something unpleasant, often (but not always) connected to physical activity (because one has to move their butt to do it).
A few examples:
Hintern hoch, runter vom Sofa, wir gehen jetzt joggen! (Get your butt of the couch, we’re going for a run!)
Du musst die Hausaufgaben sowieso heute machen, also Hintern hoch! Dann hast du’s hinter dir. (You have to do your homework anyway, so move your butt and do it now.)