Does your wife want you to remove that wall between the living room and the family room to make all that space useable? How do you go about finding out if it is structurally and or economically feasible?
You start by calling a professional licensed building contractor. They will know, after visiting your house, whether or not the removal of that wall is structurally feasible. Most builders do this initial consultation for free.
If they advise you that it is structurally feasible, ask if they have ever done this type of work, and what all is involved. If you are satisfied that they could do the project, have a plan prepared to show how the changes would be made. A detailed estimate and a scope of work would be submitted, and you would contract to do the work.
These types of structural changes always require building permits. Depending on your state and locality, only insured and licensed contractors can obtain building permits.
Check to see that your builder is in good standing and that he/she can obtain permits.