Option 1: If your trip is more than 60 days out and you're staying at a Disney Resort - using Fastpass+
The obvious first solution is to get a Fastpass (see this post for how Fastpass+ works at Disney World). Unfortunately, with the crazy demand, it's not easy - Fastpasses go very quickly.
You can make Fastpass reservations up to 60 days in advance of your arrival day he resort for your entire trip. So here's what you want to do - figure out the 60-day mark, and on that day, make your Anna/Elsa Fastpass reservations for one of the later days of your trip - the later in your trip, the better. Most people won't be able to make reservations yet since you're more than 60 days out, so you should be able to succeed. Note that the window opens at midnight eastern time - if you're particularly concerned then try making reservations at midnight 60 days prior to your arrival day!
Option 2: If it's less than 60 days out or you're not staying at a Disney resort - using Fastpass+
Non-Disney-resort guests can only get Fastpasses 30 days in advance - you're not likely going to be able to get Anna/Elsa Fastpasses for your entire group at that point. However, it may still be possible to get Fastpasses, though it takes work. Here's how - make your Fastpass reservations one-at-a-time. So make a Fastpass reservation for Mom, then one for Dad, and then one for your first kid, then one for your second kid, and so on. Often "single" Fastpasses are available for times where more than one isn't available.
The one important thing to do - make sure all your Fastpass times overlap. So if your first Fastpass time is 1:00-2:00 and your second is 1:50-2:50 you're okay. You'll have less of a time window to get there, but it's doable.
Also, don't forget you can be 5 minutes early or 15 minutes late for a Fastpass so that should give you a little more flexibility in scheduling times. So if the only times available are 1:00-2:00 and 2:00-3:00 you can arrive with your entire group between 1:55 and 2:15 and all Fastpasses should work.
Option 3: Waiting in line:
Do not - I repeat, do not go to Anna/Elsa first thing. Everyone else is doing the same thing. It's chaos, it's crazy, and the wait instantly hits 3 hoursy. And even if you get there super quickly, get lucky, and the wait is "only" 45 minutes or so, that means you've wasted the shortest-line part of the day, so the rest of your waits will be much longer the rest of the day.
So what to do? Believe it or not, your best bet (and it's still not a good one) is to get in line in the mid afternoon. The wait will probably be posted as 3-4 hours, but that's partially to dissuade people from getting in line - Anna and Elsa are only there until 5:00. The actual wait will likely be closer to "only" 2 hours or so. Sounds dreadful (and it is), but if you must meet them, this is the time to wait - the other lines in the park are long anyway at this point!
I don't really recommend this option, but if the Fastpass strategies are a no-go and Anna and Elsa are a must-do, mid-afternoon is the least-bad bet.
Option 4: Don't visit the Frozen characters!
The Anna/Elsa thing is insane. There's a weird mob mentality going on that they are a "must see." But honestly, it's just a character meet. Your kids won't have a ruined vacation if you don't see them. The 3 hours you wait in line are better spent doing other things - it'll lead to a better vacation overall. If your kids are dead-set on meeting characters and Fastpasses are not an option, you can suggest they pick between two options, both of which take about three hours:
Option 1 for three hours:
- Wait in line to meet Anna and Elsa
Option 2 for three hours:
- Meet Belle (and act in a mini-play with her)
- Meet Ariel
- Meet Cinderella
- Meet Rapunzel
- Meet Mickey Mouse
- Meet Minnie Mouse
- Meet Donald
- Meet Goofy
- Meet Daisy
- In addition, ride several rides (including all the Fantasyland favorites)
(Yes, you can do all that in three hours with a proper strategy!)
Present it that way, and most kids would take option 2!
If Anna and Elsa are a must-do for your "Frozen" fan kids, your best bet is trying to get Fastpasses in advance using the strategies outlined above. If it's not possible, I strongly recommend not trying to visit them. If you simply must visit them, head there in the mid-afternoon. The wait will still be insanely long, but it won't screw up the rest of your day.