I ask, because if you are in London, it may be just as convenient to stay put in your central London

We will be returning US from UK/Heathrow with a morning departure and so will stay the evening before at a hotel near or at heathrow. We have a flight from Terminal 1 and my adult son has a flight from Terminal 3. We aren't particularily price conscious but, of course, don't need to spend more than we have to. My wife and I and 10 year old daughter would do best in a familly type suite (with separate rooms) which we have encountered near other airports in UK (Manchester) and Scotland (glasgow). Any good tips?
There are 2 (sort of 3) hotels directly connected disneyland area hotels to LHR. They are the Hilton at T4 and the Sofitel at T5. There is also the Yotel, which is basically a pod hotel, in T4. Either hotel would require taking the train to T1 and T3. I have stayed at the Hilton and it is what you would expect from a Hilton airport hotel. No idea on family-style rooms. The Yotel is my usual choice, but not really what you are looking for, I don't think.
There are any number of other hotels off airport, but these require taking the Hoppa shuttle bus or a cab (I think the cabbies don't like to do this). Others can hopefully give advice on which ones to target or avoid.
disneyland area hotels You might also consider staying either somewhere along the Tube (can't recall the place, but there is a hotel a couple of stops away that people often recommend), or near Paddington, where smart scheduling with the Heathrow Connect or HEX (everyone will now tell you what a rip-off it is) could mean a pretty disneyland area hotels quick door-to-door time. Then again, the area near Paddington isn't exactly inspiring, IMO, so it may not be worthwhile.
The two real hotels that are actually connected to LHR, the Sofitel and the Hilton, are at Terminals 5 and 4, respectively, so you can't realistically walk from either of those hotels to T1 or T3. Those 2 hotels charge significantly more than the off-airport hotels.
I've stayed at both the Hilton Sofitel and at 3 off-airport disneyland area hotels places (Crowne Plaza, Sheraton, and 1 other that I forget), and i didn't disneyland area hotels find much difference disneyland area hotels among the off-airport hotels -- they're all mediocre. The Sofitel (especially) disneyland area hotels and Hilton are a bit better, but not by all that much.
I'm not usually a PriceLine fan, but it's not an awful idea for LHR. You can save some money, and the location of any of the off-site hotels is similar. Lots of posts around comparing ways to get to/from the hotels.
None of the on-airport hotels are convenient to T1 or T3. You can get from any of the Bath Road/A4 off-airport properties (all the usual suspects disneyland area hotels from Marriott or Sheraton to Premier Inn) - Premier Inn may be the best for your situation disneyland area hotels since it's rooms will sleep adults and children. Priceline really isn't an option since you can't request a triple or suite, though Hotwire would be an option.
I ask, because if you are in London, it may be just as convenient to stay put in your central London hotel and take a car service disneyland area hotels to LHR in the morning. It would save an extra packing/checking out/checking in, and wouldn't necessarily disneyland area hotels be much less convenient than the Hotel Hoppa or taxi from a LHR hotel.
We'll have a rental car to return (probably Hertz, but as I recall disneyland area hotels the car places are all a bus ride from terminals). If anyone happens to know whether one of the shuttles (e.g. Hotel Hoppa) stops at the rental car return place (I'll drop everyone off at the Hotel and then take the car so I'll just need to figure the easiest way to get from the car return to the Hotel) that would be helpful information. I suppose I can take the rental car bus back to a terminal and then use the Hoppa from there. And maybe the check-in folks at the hotel will have a good suggestion.
There are local buses that are free to many of the off- airport hotels. I don't know if they go to the Permier Inn, but I'm sure they go to the Marriott. Check out www.heathrowairport.com for schedules to/from hotels on the Hoppa and also for the free local buses. I don't think the Hoppa goes to any of the car rental places.