Keep in mind that having a 10K rated hitch does not mean that motorhome is actually rated to pull 10,000lbs. Motorhomes are made up of a bunch of purchased components and like a chain the weakest one deteremines the strength of the whole. My DP has a 10K hitch but due to transmission limits is actually only rated to pull around 5K, depending on how much stuff is in the coach and with 11 kids you will have a lot. If the motorhome has a hitch that is only rated for 5K that is probably all the the chassis is rated for. The other issue you will run into is that most motorhomes that I have seen are designed for families on a budget and sacrified towing ability for price or they are designed for retired couples and only have sleeping for a handful of people. A tour bus may be your only real option for 13 people. My motorhome is rated to sleep 9 but I really don't know where I would put that many people while traveling. Some would have to be in beds. Actually, I really don't have a huge problem with that and often sleep in a bed if I have a competent alternate driver. It some states thay have to be over 16 to do it legally.
And I think that it was stated before but we need to be clear that with a van you have four options for towing: 1) Add 4wd with a transfer case that includes a neutral, 2) Get the drive tires off of the ground with a dolly or trailer. This one has a catch, there are not many dollies that will hold a van and the trailer would add another 1,500lbs to the rig plus you have to find a place for it when you stop. 3) Remove the driveshaft. This can be a real pain in the best of conditions. 4)Get a driveshaft disconnect. I really don't know much about these. Towing with the drive tires on the ground without doing one of these will destroy the transmission in the van.