Arriving Dublin via Aer Lingus and then on to Edinburgh on same carrier. Will I be required to clear immigration and customs in Dublin? Also is 1 hour 10 minutes enough time?
There will be a passport check in Dublin but not in Edinburgh - as long as everything runs to schedule 70 minutes is OK
Aer Lingus and their partner airlines are great, IMO. I'd happily fly them any time. Just be aware the Dublin airport routes you through a big duty-free shop where you could get distracted and lose track of time.
Also, if you're taking the same route homeward, you have to clear US passport control in Dublin before your flight. When you arrive in Dublin (or Shannon) from Scotland (or elsewhere in Europe) you have to go through "US Pre-Flight" which can take an hour depending on how many passengers are ahead of you. It's not optional -- you can't skip it and go through customs upon landing in the US instead.
Aer Lingus flights from Dublin to Edinburgh and Glasgow leave from gate 336 and 337. The problem is that you will see signs for gates up to 335 in one direction, and signs for gates over 400 in another direction, and no signs for 336 and 337. Just follow the signs to 335; soon, you'll see the signs for the gate you need. It's a 10-15 minute walk, so don't dawdle.
One hour and 10 minutes should be enough, but if it's not, there are several flights per day on that route, so they'll put you on the next one. Assuming, that is, that you are all on one ticket.