I am a Dual UK/US Citizen and my DH is a US Citizen, married for 10 yrs and lived in the USA the whole time. Don't have children so I can't help you regarding children but as you already have passports for them they are sorted.
Here is what I included in my DH's Application, PM me with any questions, I am more than happy to help and give you some examples of docs that I included. Some of your wife's paperwork will differ than my DH as he has a Police Pension but it will give you a guideline.
Anyway here is a link to my list:
http://talk.uk-yankee.com/index.php?topic=52460.0Step 1. Get all the required documentation together before applying as it less stressful to have have it together beforehand than to be scrambling at the last minute.
Step 2. Apply online for the Spousal Visa and ask in the comments section for the KOL (REQ).
KOL (REQ) allows your wife to take the "Life in the UK Test" after arriving in the UK straightaway and then apply for ILR which can be done immediately after you get the test certificate. The only documentation you should need for ILR is proof of your acceptable living conditions and proof of funds.
If your wife can fly back to the UK before she applies for the Spousal Visa and takes the test then she can apply for Permanent Residence from the USA and skip the ILR. Depends on costs of the extra flight/time versus the extra money needed for the ILR visa once you get to the UK. Not sure how you apply Stateside going this route as MY DH asked for the KOL (REQ) and will do what he needs to do once we are home. Extra flight back for him was the same price if not more than the cost of the ILR Visa which is why we chose KOL (REQ).
Step 3. Send all your documents via mail (slower, could take up to 3 months to process) or courier (fast, DH got his visa the same day) to the British Consulate in your area.
Step 4. WAIT !
Step 5. Fly home