Heathrow Terminal 3

Honestly, it's a very easy process.

First you go through passport control. Have your passport handy and follow the line for US citizens.
Next you go through baggage claim.
Then Customs, although usually this is a just a walk through since you probably won't have anything to declare.

Pretty soon you will be heading to the arrivals section. It's usually quick and easy. I just went through a few weeks ago with two grandkids, and it took no time at all. And hopefully you have gotten your ETA already. If not, you can find out more about it here: https://www.gov.uk/guidance/using-the-uk-eta-app

Follow signs to border control. Then collect your bags from the carousels. Then exit via the Nothing to Declare exit.

Don’t forget you all need ETAs unless you are British or Irish.

After that you go through the Duty-Free shop

Duty Free shopping is airside not after customs.

vvece, let us know if you need any help getting to your hotel. :-) I know London can be confusing at times, and having small children with you can make it a bit more difficult.

My experience flying Delta into LHR Terminal 3 is my arrival gates are a LONG walk to the arrivals hall, where you go through passport control.
There are men's and ladies rooms along the way, so you can take a break if the kids (or their parents) need to answer the call.
The rest is very simple and straightforward.

I just did this walk yesterday and I will echo that it is a long walk. It took us about 10 minutes…maybe a teeny bit longer. There’s a couple of moving walkways on the route to speed things up. There’s plenty of chairs to sit down in if your kids need a break part way through. When we got to the immigration area, US passport holders were sent off with the EU/UK passport holders to machines for immigration. You place your passport facedown on the scanner, stare into the camera, wait a second, and then the gates open for you. You proceed ahead and around the corner and you come to the baggage claim hall.

You cannot use the automatic machines with small children. You will be directed to a Border Control officer.

That’s a really good tip to add - because I was wondering about that. My husband is super non-techy and he could not make the machine work and there was someone there to help him and offer direction to others.