Suggestions for stops

One possibility if the weather cooperates would be to head north from Dingle - drive over Conor Pass and up to the Tarbert Ferry. From there you can continue up the N67 along a very pretty stretch of coastal road all the way to Doolin, which might make for a pleasant overnight stop. It's the drive itself that's the attraction. Lots of pretty little places to stop along the way to stretch your legs and enjoy the beautiful seascapes, meandering along and taking it at your own pace. The village of Kilkee would be a good place to stop for lunch. There's a nice stretch of beach there and a short cliff walk that makes for a nice photo op. It's one of our favorite scenic drives in Ireland.
You'd be driving along rural "N" roads so it would be relatively slow going but you probably won't care - this is one of those times where it's more about the journey than the destination.
Depending upon your particular interests there's a late afternoon/evening excursion by boat from Doolin to view the Cliffs of Moher at sunset. There are a couple of great pubs featuring trad music in Doolin as well.
Next day you could head back to Dublin via the modern motorway, with perhaps a stop at the monastic site at Clonmacnoise.

Those are great suggestions- We will do them in reverse. We are flying into Shannon and out of Dublin so we are actually starting in Doolin 2 nights then the ferry route to Dingle and stay in Dingle for 2 nights - we then have 2 days/nights to get to Malahide. We are staying in Malahide 1 night before we head in to Dublin for 2 days.
I am stuck on Dingle to Malahide. Any suggestions for that route?

Well, if you're not already planning to drive around the Ring of Kerry that would be an obvious suggestion. Your Mom might especially enjoy a jaunting car ride thru the Gap of Dunloe. The Gap is one of the prettiest little glens in Ireland and doing it on a pony trap, especially if you get a particularly talkative driver, could make for a lasting memory for all of you.
The starting point for the trips is Kate's Kearney's Cottage - a good choice for lunch.
I'd avoid Killarney if at all possible - traffic getting in and out can be murder around midday.
The ROK itself can get crowded once the tour buses are on the road, but a very nice diversion is the Skellig Ring Road that loops around towards the village of Portmagee. The tour buses still don't go out there so it makes for a pretty mellow experience. Possible stops along the way are the Skellig Center located across the bridge from Portmagee, Valencia Island, the Kerry Cliffs, and the pretty village of Ballinskelligs around on the southern side. It's where the monks from Skellig Michael relocated to when they left the island. There are the ruins of an old Abbey there along a nice stretch of beach. Another attraction not to be missed if you're nearby is the Skellig Chocolate Factory located just down the road from the Cliffs.
Depending on your interest and your stamina you could continue south from Kenmare and just meander. One nice off-the-beaten-track place is the village of Baltimore - very picturesque and a place with an interesting history. It was the site of the last pirate raid in Ireland back in the 1800's. Apparently Barbary pirates raided the town and virtually depopulated it - took years for it to regenerate itself I'm told.
For your last day enroute back to Dublin you could explore the seaside village of Kinsale, although it may not be the best choice for your group due to the crowds that descend upon the place when the tour buses are rolling. That said, just south of the town on the way to Charles Fort is the little hamlet of Summercove - home of Bulman's Pub. Very convivial place and located right on the harbor.
There's another monastic site at Glendalough on the way back to Dublin. It can get crowded too, but you can see quite a lot of it as a drive by if you don't feel like fighting the crowds. Another scenic drive with lots of photo ops along the way is the Old Military Road (R115) heading north from Glendalough. It's a typically narrow Irish rural road, but a very pretty one if you have the time and the interest. A possible short detour is the village of Glencree - there's an old WWII German POW cemetary there that's quite evocative, and there's an old Mass Rock nearby that requires a short walk along a pretty stream.

Look at Adare? Lots of cuteness going on there. Or Cahir, with its castle and nearby Rock of Cashel? Or Kilkenny? I would enjoy any of those for an overnight.

I will check them all out! Thank you.