Is Surgery the Only Solution to Fix Mandible?

Often the hyperactive tongue is the reason that teeth tilt or flare.  Even if braces are worn, the tongue issue must be addressed.  Consulting with a speach therapist can help and should be considered.

Often the growth of one jaw vs another is so dissimilar that surgery is needed.  Prior to doing so, get at least one more opinion, but it is possible that there is not other way.

I approach bite problems with the "functional jaw Orthopedic" technique.  The best time to influence the dental arches is early in developement as one's face and jaw are still growing.  This gives us time to expand the upper arch (maxilla) and to upright teeth and advance the mandible (lower jaw).  By using expansion appliances, either upper or lower, we can influence facial profile, TMJ position, tooth position, and tongue position which all influence speech, health and self- esteem.  70% of the children I see in my practice have under-developed arches.  This means the arch form is too narrow and the lower jaw is too far posteriorly positioned.( too far back) This is called early interceptive orthodontics and is MUCH MORE EFFECTIVE, stable and painless than surgery. Look for a DDS, pediatric dentist or orthodontist that is trained in functional appliances. You and your kids will be glad you did !!!

From your description it is very difficult to ascertain exactly what the situation is.  Perhaps the lower teeth lean outward because they are overcrowded, or perhaps they do so because of an tongue posture issue.  Also, the degree of lower jaw retrusion is highly variable in "overbites" and often the upper jaw plays a role as well.  There are appliances which are capable of helping the lower jaw adjust it's position forward, and there are new adjuncts for braces which are excellent anchors for pulling protrusive upper teeth back.  The bottom line is that in general surgery is a last resort, we are getting better and better at avoiding surgery, but sometimes it is the only way to get a good result.  You should seek several opinions about your case so that you are confident in making your choice about which way to go. 

Many cases with an overbite and a recessed lower jaw are mistakenly diagnosed as a problem requiring surgery to bring the lower jaw forward, where the actual problem is that the lower jaw has become "trapped" behind the upper teeth during development and ends up "displaced" back-word out of an ideal position.   This ultimately can lead to TMJ Dysfunction and even Obstructive Sleep Apnea in later years if the problem is not addressed correctly at your age.  Make sure the orthodontist is taking TMJ Tomograms at minimum, and can show the lower jaw (condyles) in a normal position.  If they don't understand your concern, get another opinion from an orthodontist/dentist who works with TMJ Dysfunctions.  They may see the problem as it most likely is, that of the lower jaw is being "trapped" into its recessed position and will work to see that it is brought forward into an ideal position, eliminating the need for any surgery.  I hope this is helpful and that you seek truly an expert opinion on this tricky problem.  After-all, you can't undue surgery, except by another surgery!

Really impossible to know. 
Almost everybody has some degree of skeletal disharmony, but only the most severe require surgery.  Many of the moderately severe ones can be treated either way depending on how much compromise you are willing to accept.  Get a 2nd opinion from an orthodontists (not an oral surgeon) before you agree to surgery