We have driven in Ireland before and we know that we will also be jet lagged when we get there.

Is it possible to get from the airport to Trim on the smaller roads without using the major Motorway? We've been trying to figure it out with the maps, but would appreciate any and all suggentions.

That said, let's not get nasty----yes we CAN take the major Motorway, but we'd just prefer to take our time on the smaller roads for this part of our trip.

Cowboy1968--- are you out there? You have been helpful in the past for driving directions. Any comments?

Sorry, TPAYT, I'm afraid I'm not of much help here.
In the Greater Dublin area I usually stick to the major highways and motorways.

It is quite easy to get around the Southern perimeters of the airport on the Old Airport Rd (not knowing where you will have to pick up the rental car) without using the motorway. Old Airport Rd is a not numbered road connecting R132 (which runs north-south alongside the airport) with R108. Basically, you always stay parallel to the runway and the airport fence and have both on your right side.
When R108 hits R122 you go North, until you hit R125 which you would take West.
Stay on R125 until you get close to Trim where you hit R154.

It would be easier to follow directions from the airport to Swords, i.e. take R132 north, and R125 from Swords all the way to Trim, but you would have to find your way thru Swords.

Honestly, neither option is what I would recommend after a red-eye flight and with jet lag. The immediate surroundings of Dublin airport are not that scenic that a longer drive on smaller roads would add much extra benefit. But that's for you to decide.
I just don't want to hear any complaints later about getting lost on day 1 already ;-)

Cowboy1968----thanks for the info. After your opinion, we are checking the map with your directions. We probably will stick to the major highways.