9 Day Ireland + North Ireland Itinerary...too ambitious?

It would help to know what your interests are, but you're trying to cover the whole length of Ireland, from the Giant's Causeway to Dingle Peninsula, in 8 days. That is too ambitious, IMO. I would choose north or south, and since Belfast is a must-see, north is the obvious choice.
Have you look at the feasibility of flying home from Belfast? There are very few direct flights to the US. And you'll almost certainly want to return the car in Dublin to avoid the fees of returning it in Belfast.
My suggestion:
Arrive DUB, pick up car, stop in Trim on way to Belfast. Two nights Belfast.
Causeway Coast to Derry. Two nights Derry or nearby Letterkenny.
Donegal for Slieve League cliffs, etc. Two nights Killybegs.
Overnight in Athlone for Clonmacnoise, castle and old pub.
Drop car at DUB and take bus into Dublin for remainder of trip.

I think this might be a bit much. Galway to Belfast appears to be at least a four hour drive, even without the stops. Visiting Giant's Causeway and Carrick-a-Rede is normally a full day activity (along with other sites along the Causeway Coast) so as it stands you wouldn't really have time to see Belfast itself. Is Belfast a must-see for the city itself or for the Causeway Coast?

I would concentrate on either Dublin + west coast or Dublin + Northern Ireland, and if Belfast is a must-see then I think that helps you decide!

There are (or at least were...) direct flights from Belfast to Newark so flying home from there makes sense.

Good luck with the rest of your planning!

Thank you both for your input. We looked at our itinerary again with your feedback and agree it's probably best to edit it down! We will either stay within Ireland (Dublin - Galway) or we will stay on the east coast (Dublin - Belfast). We are reevaluating to see how much of a "must see" Belfast is for this trip. :-)

There are no flights from Belfast to anywhere outside the UK or continental Europe. The flights to Newark ended well before Covid. Rather than connecting somewhere you'd be better returning to DUB for a direct flight from there.

If you can, fly into Dublin or Shannon and then home from the other, so you aren't backtracking.

We haven't been to Ireland in 20 years, but we did two trips in the early '00s, one where we flew into Shannon, did a southerly route and flew home from Dublin. Then a couple years later, we flew into Dublin, headed north and west and flew home from Shannon. We hit Galway on both trips and were glad we did. The first trip, we were so overwhelmed with having just landed, driving on the wrong side, etc., that Galway wasn't very enjoyable. The second trip, it was our favorite place other than Dingle. But everywhere was awesome, honestly. We have been very hesitant to return because I don't think it will be the same now with the increase in tourism to the island.