Connection time in London Heathrow and baggage claim

We went through Heathrow about 4 years ago. It took us so long to get through customs that ,when we got to the baggage pick up, everything was gone. We were lucky to see someone at the American Airlines booth. She told us to look at US Air site. They were sitting by themselves there. Don't know what happened but we came into Heathrow at a very busy time with only 4 booths open in customs. I think it is one of the hardest airports to get in and out of.

Gentlemen, you are confusing customs with immigration (passport control).
Customs is AFTER baggage pick-up (it has to be, otherwise how could they check the contents of your bags?). But, there is no customs between Ireland and the UK, they are both members of the EU. Even coming from non-EU locations, customs just involves walking through the "nothing to declare" channel.
Immigration (passport control) is BEFORE baggage pick-up, but there is also no immigration between Ireland and the UK, they have a common passport area.

To get to the point. Are your two flights to and from the same terminal at Heathrow? I guess not. Even without immigration and customs it can take up to ½ hour from when the plane lands to when you get out of the terminal. Heathrow is that big and involves a lot of walking. Then you (probably) have to change terminals (~1 hour, they are not all in the same place). Then you have to check in again, and for a long distance flight the requirement may be 2 hours before departure.

CONCLUSION: If this is two separate tickets, no way.

It looks like your flight from Dublin arrives at Terminal 2 and your flight to Salt Lake departs from Terminal 4. As has been mentioned, these terminals are nowhere near each other, and it takes a long time to get from one to the other. This connection - especially on two separate tickets - would make me extremely nervous.

Since it sounds like you already have your tickets (is that right?), the best advice I can offer is to try to change/rebook to an earlier flight out of Dublin.

Thanks for the comments. Almost pulled the trigger on purchasing the Dublin-London Heathrow ticket but didn't because of this concern of lack of time. We already have the ticket from Heathrow to Salt Lake. I will take your advice to get an earlier departure. I also appreciate the correction on passport control/immigrations vs. customs. Nonetheless, it looks like we need more time for the transfer between flights for our transport between terminals (you are correct with terminal 2 and 4), getting our baggage and rechecking, and security and passport control. We don't want to stress it. Thanks.

In going to Europe for 13 of the last 14 years, we now go to the city that we are flying back to the US from and spend one night there in a hotel near the airport. This developed after having to catch a 0430 flight to get to our departure city for the flight to the US. We said never again.

To go from terminal 2 to terminal 4 landside you have the choice of a bus or the shuttle train at the Heathrow Express station. It could easily take 1.5 hours from landing to get to the check-in although you may be fortunate to do it somewhat quicker. You have to then clear security and get to the gate and some these at T4 are very remote.

Can you do it on a good day in 2.5 hours? Yes.
Would you be able to do it every day? No.
Could you have done this on a single ticket? Yes as you would transfer airside.

I suggest reading what Rick has to say about packing for travel. He routinely lives out of a carry-on sized bag for months at a time. My wife and I did two weeks in Italy last year in carry-on sized bags. (By the way, it was liberating!)

If you carry your luggage on the Aer Lingus flight, you'll have a MUCH better chance of making your connection in London. Just make sure your luggage meets Aer Lingus' carry-on size restrictions (generally a little smaller than US airlines).