This sounds like a great idea and one that I have on the list for when time and money permit.
There are two main approaches: Use an experienced agency/shop/site to co-ordinate it all for you and a DIY. Whilst an agent will charge a fee, they
should have insider knowledge and a range of fares and hotels that you could not find in days of searching online.
Also, if you buy the tickets piecemeal (both travel and hotel) you may find many of the websites charging you that dreaded booking fee each time. An agent, ought to be able to charge you in one, or bite sized chunks to avoid some of those charges.
You will also find that RTW packages can be put together on the web site of the airline alliances: Here are two of them:
oneworld and
Home - Star Alliance but don't forget Sky Team. If you look through the carriers in each group - you will get an immediate idea of their scope and routes. At a quick glance, they all have RTW planning/booking buttons on their front page.
Lastly, you might want to consider method of payment as regards accruing Frequent Flyer Miles, likewise, if you go with an alliance RTW. There is an opportunity to haul in an enormous amount of FFMs. The trick being to plan the expenditure and not make a purchase soley to get FFMs. But a credit card that has points that can be exported to the chosen alliance group, will make a huge difference by directing all the points into a single pot. Not for this trip but for the next!
We look forward to hearing the choices - in a few months time!
ps It occurs that, on such a long and complex trip, you will have a considerable amount of paperwork and/or confirmation numbers for various bookings. I would suggest planning to scan all of them and take them with you on a USB stick. Further, I would cache the files online (password protected) so that if you lose your bags (even temporarily) you would be able to recover booking and itinerary information.
When travelling alone or in a pair, it's one thing to 'busk it' but not with children. Also, add copies of health documents, innoculations etc. Whilst most authorites will want originals/replacments, if you can print out copies to show them (whilst waiting for replacements) it will greatly reduce the hassle. I am currently planning a six week RTW (although mainly NZ + OZ) and will be doing this even though only two of us travelling.