Encourage your kids to study these two resources, commit as much as possible to memory, and discuss the main points with her using questions to draw her out.
http://ajwrb.org/watchtower-approved-blood-transfusions
http://ajwrb.org/do-jehovahs-witnesses-really-abstain-from-blood
Ultimately, they have to respect her choice, but they certainly have both a right, and a responsibility to try and be sure that it is an informed, and voluntary choice. The same can be said of the doctor that is treating her.