Yup, you really don't want to go with the Charters. The last time I flew on a charter (3 years ago, London to Calgary in Canada), the leg room was awful, the shoulder room even worse and not much of a head rest (fairly low seat back). If you bear in mind that I am 5'4" (and a size 10) this is very worrying for people who are any taller or wider than me... (some women and most men are). Charters are okay for European flights, but I wouldn't do one again for a transatlantic flight....
Yes AA are supposed to be very good for leg room: they recently had an initiative to introduce extra legroom throughout their economy and business classes. I believe you should be able to safely expect about 34" (not sure if, realistically, you will get 35/36") - noticeably more that BA/Virgin.
When you check-in, it might still be worth trying to check-in early and asking if any exit row seats are available for you and your husband - your children could sit in the seats immediately behind. Its worth a try, although I don't know if you will be able to get 4 seats together like that.
Boo