Yikes, $7,000 for that horse. I too recently bought a horse after nearly 18 years of not having one. My dear, how things have changed. I saw a lot of horses and notificed people are trying to sell based on pedigree to justify the cost and so many dishonest people out there.
Perhaps, it would be wise to start the kids with riding lessons or lease a horse to find out their interest prior to horse shopping.
I bought my horse with a 30 day trial guarantee. So, I paid 1/2 of the total purchase price and when I decided to keep the horse, paid the balance. Prior to purchasing the horse, I went twice to ride the horse before I brought her home and all seemed fine.
During the 30 day trial period, I noticed a few bad habits that I had not previously detected. The big one, was ground tying and bucking on the trails. So you see, I could have got my money back. Incidently, I kept the horse, but she was a lot more work then I imagined. It might be helpful to see if the seller is willing to work out a similiar arrangement with you.
Good luck and happy horse looking.