I didn't do a tower, but I will comment on the timing, based on what someone else posted some time ago: If you book the tower ascent for about 1 hour after your entry for the church, you will probably have just about finished seeing the lower part of the church. If you have not, you can finish up with the lower level after descending from the tower. There's also a small museum and quite an attractive shop. Once you enter the shop, you cannot go back to complete your sightseeing.
I am nervous disagreeing with Enric, but I think having the first entry time at La Sagrada Familia is helpful because when you walk in, the only people there will be others with the same entry time. At other times of the day, when you arrive, there will be a lot of holdovers from earlier time slots. So I like the idea of the first entry there. The Tourist Office told me that's a popular time and that I should book 48 hours ahead of time in early August to be reasonably sure of getting that time slot.
It's my vague impression that the towers are about more than the view--that you get a close-up look at interesting parts of the edifice. But as I say, this is not first-hand information. If you Google "which tower", you'll probably find some comments from earlier visitors. Kids do usually like to climb, so I think a tower is probably worth the time and cost.
The point about possible heat at Parc Guell is a very valid one. I was able to schedule it first thing on a different day, so I didn't have to contend with midday conditions. The downhill walk back to the center city should be very nice, but probably best not at 1 or 2 PM. One thing to consider, though, is that you have a really packed schedule. I'm a wanderer by nature, and Barcelona's architecture is made for strolling, so I hope you have time to do some of that. If you pre-book too many time-specific site-visits, I fear that you'll always be running to the next obligation. But that's a pretty long walk back from Parc Guell and--in truth--I question whether you have time for it. With a group of 4 I'd at least consider a taxi.
You mentioned churches. The Barcelona Cathedral is in the Barri Gotic. It's free part of the day and has an entry fee at other times. I don't remember the details. Santa Maria del Mar is also often mentioned. This website will give you some other ideas. I'd circle the interesting-sounding ones on my map and take advantage of proximity to see a few.
Enric, is it necessary to buy tickets to the Sant Pau modernista site ahead of time now? Perhaps I hit a fluky August day, but I don't think I saw more than 10 other tourists the entire 2 hours I was there.
Edited to add: Casa Mila and Casa Batllo are to me quite different from art museums, but I do love art nouveau, so I'm biased. If I were you I'd wait until I'd been in Barcelona for just a little while and seen how everyone feels after seeing one or two other modernista sites. I believe you'll be able to get a ticket to one of them on two days' notice. If you run into a problem, you can still enjoy their fabulous exteriors. The Palau Guell would be another possibility, not as heavily visited though it would be best to buy the tickets ahead of time, because I did see a bit of a line.
I don't think a HO/HO bus is a great idea. Perhaps on a weekday if will be OK (though I assume rush hour traffic would be quite a drag), but when I arrived in Barcelona around noon on an August Sunday, there was a line that looked about 200 people long at Pl. Catalunya. They were waiting for the HO/HO bus. Not a good use of time or money. Also, you'll probably be sluggish that first day; I think you'd do better to keep moving. You might check into a walking tour for that day. Don't make arrangements ahead of time, but know whether something is available and how you would hook up with it.