I would get multiple opinions, for price as well as examining/comparing what the different orthodontists say needs to be done....do ask lots of questions, make sure they explain to you each step of the planned process, for each child, and ask for cost estimates, just as you would with anyone doing work on your house. I was lucky, my Gandfather and Uncle are my dentists, and an aunt and my mom worked as hygienists in their office, so I had the best care, in my best interest, for free.
I really needed braces, I had teeth too big for my smaller sized mouth, and a cross bite, I had used a pacifier 24/7 for the first 3 years of my life, which didn't help. From 3 years old, the minute they got me to give up the Nuk, I had expander appliances in my mouth, that widened my upper palate and lengthened it. Different ones every 6 months or so, mine were not cemented into my mouth, even at age 3 I had a removable appliance, so I would be able to remove it to brush really well, and remove it to eat, to avoid decay/food getting trapped beneath the appliances. I only lost one, and had a few near misses at school, accidentally tipping it off my lunch tray into the garbage - I spent a few hours later going through all the cafeteria garbage bags to find it , take it home and sterilize it and have to wear it again, and never did that again!
Then I had braces from 11 years old ( had all permanent teeth by them) to 14 years old, also had headgear to wear to bed, and an expander in my upper palate at the same time as the braces....I do still need ot wear my retainers at night a few nights a week, and I am 32, now. But it was all worth it, I have only had to have my 4 wisdom teeth pulled, if they had left me alone, I would have had to have about 6 regular permanent teeth pulled, as well, just to make room for the rest. All this dental work made me very aware of my teeth ( as well as my dental family - 3 dentisits and 3 hygienists in the fam) and I have not had one cavity yet.
My husband's parents did braces on his two older sisters, but then let him choose at the age of 11 if he wanted them - well, of course he said no, he was a kid and wanted to be cool. Now he wishes he had had them, he even has 2 residual baby teeth hanging around in his mouth - he has a small jaw with lots of crowding in the lower front, and none of his teeth are straight. Unfortunately he is not one for pain, and although he wishes he had done it in the past, he is too chicken to get the teeth taken care of now - I wish he would, though, since my family would probably take care of it for a big discount, or for free.
Anyway, gather lots of opinions and gather all the information you can from each one, and then compare and choose the plan that is right for your kids.