Alright Jobber,
First here is your coverage ratings:
Carrier Avg. Rating No. of Reviews Towers Coverage Map
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1. Verizon 2.18 45 Towers Map
2. T-Mobile 2.11 35 Towers Map
3. Sprint 1.83 36 Towers Map
4. AT&T 1.69 26 Towers Map
AT&T is the worst in your area, but you should be okay on any of these, particularly if they have free roaming.
First lets look at family plans:
The cheapest you could do is Metro PCS, but they don't have the iPhone. Unlimited mins/texts + 5GB (2.5GB per line) of data for 2 phones runs $95.
If you switch over to T-mobile's prepaid side, you'd be looking at $99.98 for you and your wife getting unlimited calls/texts and 2 GB of data. If you add in your kids phones, that would bump you up to $119.98. No phone subsidies on the prepaid side of the house though, but you can finance a phone at 0%, and if you call them perhaps they can forgive the ETF if you're staying with them, just switching to prepaid. Worth a shot at this first IMO.
If you go to Ting, you're looking at 3000 minutes, 1000 texts, and 2 GB of data for $111. If you add in the kids it jumps to $123. You guys use your phones just a bit too much to make Ting worthwhile imo. If you cut your minutes down to 2000 and your data down to 1GB, you'd be at $76. Plus while the iphone5 will now work on Ting, it isn't officially supported yet so you'd have to jump through some technical hoops to get it to work.
Now, lets look at individual plans (where you just forget about the kids altogether):
If your wife can live without the iPhone and with a GS3 again, then you'll save the most with Voyager Mobile. They offer Sprint coverage (no roaming though), unlimited talk/text and 5GB of LTE data for just $39 a phone. This is $78 total.
Another option would be Straight Talk (T-mobile version). Again, no roaming, but for $45 a line you unlimited talk/text and data is supposed to be unlimited. In reality they throttle you around 2GB a month, but you should be under that limit anyways. No LTE with Straight Talk though (even when you go through Verizon/AT&T for Straight Talk). This is $90 total. Net10 wireless offers this exact same deal and are owned by the same company. But you can actually find AT&T sim cards if you want AT&T coverage, Straight Talk stopped selling them and people now price gouge for them on Ebay and the like. Since AT&T apparently has the worst coverage by you, this is likely irrevelant.
Another option would be Solavei (on Tmobile's network). $49 a line gets you unlimited talk/text and 4GB of data (at HSPA+42 speed, throttled to 2G past that cap). They have roaming (on AT&T) and they are adding LTE coverage as T-mobile rolls out its LTE network. If those are big issues for you, you should consider them. Also, if you refer 3 people, you get $20 off your bill every month as long as those folks are with Solavei. So, if you like that sort of thing, you can really cut your bill down.
And finally, what to do about the kids:
One company specializes in phone for kids... its called kajeet. You can lock them out of "inappropriate sites", track their location, and do all sorts of privacy invasion things that only a parent would want to do. Their plans are a bit overpriced, but if you want these features, they're the only game in town.
Another option would be to put the kiddies on Ting. 2 phones with you can share 100 minutes and 1000 texts for just $20 a month total. Might be something to consider.
ETA: With Straight Talk, Tmobile, and Solavei, you can keep your existing phones and use them by swapping the sim card. With the others, you're going to be buying new (or used) phones for service.