Real drive time- Dublin area to Belfast (Titanic)

It's Motorway the whole way so that 1+45 should be about right...barring any unforeseen delays with traffic, parking, etc.
Suggest getting there early, ie when it opens, to beat the tour bus crowds that start to roll in around 10:30 AM. It's a terrific museum...worth the drive.
Can also take the train from Dublin and taxi over to the museum if you'd like to spare yourself the ordeal of driving, parking, etc.

Thank you! I have purchased Titanic tickets for a Sunday so I hope that means the traffic will be a bit more forgiving!

Traffic should be minimal, especially with an early start, but it will be more crowded on a Sunday.

I am hoping to get there fairly early to see the exhibits; we also are doing afternoon tea at Titanic. I can't wait!

After you finish the museum tour (and tea) you might want to wander around the old Harland & Wolff shipyard buildings adjacent to it. Not sure which (if any) are open now, but you can at least peek in the windows of the old design building where Andrews and his group of draftsmen designed the ship and oversaw construction.

There's also the "Nomadic" - one of Titanic's tenders that was used to ferry departing passengers from Cherbourg before the fatal voyage - including Molly Brown (but not Jack or Rose).

Definitely not 3 hours. Closer to 2 at most. We drove all the way to Crawfordsburn, northeast of Belfast in under 5 and we stopped at Trim castle for a couple hours and also made another stop en route.