My husband and I are taking our sons, ages 7 and 11, on their first overseas flight on June 26th. We'll be flying from Austin to Heathrow on British Airways and will land at 10 am. We were originally planning to spend some time in London and then travel around England and Scotland for a month. Our plans have changed, however, and we will instead catch a plane from Heathrow to Edinburgh. Since we didn't book the flight to Edinburgh when we booked the London flight, the flights are going to be on separate tickets. I haven't travelled to Heathrow in years so I'm not sure how much time we need to allot for the airport transfer between flights. I would like to also feed the kids during the break. How much time should I allot between flights? Is it possible to transfer between flights without going through customs in London? We'll probably be checking at least one bag so we'll need to deal with that as well? If we book a BA ticket can I call the airlines and ask them to transfer our baggage between the flights so we don't have to deal with baggage claim?

A couple of hours.

No. Immigration (the check, I think you are incorrectly referring to as 'customs') will be done at Heathrow as the subsequent flight is a domestic flight. Customs checks would apply too if the bags are checked to LHR. If the bags are checked through, then the customs checks would split (in theory) in two: Carry-ons would be checked at the port of entry (LHR), whereas checked bags would be controlled where they are delivered (EDI). Generally, checks of both checked bags and carry-ons are generally made at your final destination. It's not a systematic control. They may choose to pull you out or, if you have anything to declare, you'd go through the red channel.

Unlikely. Even on two BA tickets, it is unlikely that they'll check the bags through.

My personal tip would be the following:
The BA flight from Austin arrives at 10 am. You head to arrivals, go through immigration, pick up your bags (in the highly likely case that they won't be checked through, drop them off at a (self)-check-in desk (you can drop them of any time on the day of travel), take the Heathrow Express or the tube into central London, have lunch somewhere, go to a museum or place of interest, and take the Heathrow Express/Tube back in the early evening to catch >8 pm flight to EDI.

That way, the risk is relatively low in case something does go wrong and you have essentially two ways out this can play out. If the AUS flight is on time, then you have a nice day out in London. If the AUS flight is late, then you'll just stay at Heathrow, but you may still make your flight to EDI.

Not sure that's correct. If the flight to Edinburgh is in economy, you can't drop the bags at any time, bag drop will only be available for that flight three hours before departure.

I would allocate at least three or four hours between these flights. You�ll need to retrieve your bags and then recheck them. BA does not interline luggage on separate tickets. Note that if you do not show up for the EDI flight for any reason, that whole return ticket will be cancelled, forcing you to buy new ones (or not travel.)

An option would be to check the bag(s) under one of the adults so that on arrival that adult clears the UK border, collects the bag(s) and then rechecks it in whilst the other family members go the flight connections route and remain airside and clear UK immigration during that process. You can then arrange to meet back up in the departures area.

*bags - assuming that the number of bags is within the allowance of one person of course. If it is more than that then you might as well all just all go through immigration / bag collection etc together.

BA expressly will not check the bags across tickets (this does not interlining, because it is BA-BA). Thus, it is close to a certainty that OP will need to claim and check them at LHR.

Because of the no show risk on separate tickets, I would always allow at least triple the MCT. This accounts for all but very serious delays. The idea of trekking around London for the day is a good one, but you do have to consider whether the two children will be in any shape to do so if they have had a very short night of it on the hop from AUS to LHR.

Not sure how this will work. The CI agent is certainly not going to check more bags than the individual allowance if only one passenger of a booking shows up for the LHR-EDI check-in and checking in bags for each passenger in the booking may fire backwards if the CI wants to see passports of all passengers while those same passenger are staying airside.

Re: bag drop. It is indeed 3H for non-status holders and from 5 am for status holders. Can't say much about the self-check-in machines as I haven't used them (generally traveling HBO or there was an actually check-in desk immediately available).

No really, KARFA is right. You can now, "during a trial period" drop bags at anytime in any class of travel.