My condolences for your loss.
Unfortunately, however, you’ve been mislead. There are a lot of misconceptions about the new Post 9/11 GI Bill and how it can be transferred to family members. Currently, a service-member must initiate a transfer of educational benefits while still in the service. Even then, the benefits can only be transferred to a spouse or child, and not to any other family member.
There is a program that might be the cause of the confusion. The Dependents’ Educational Assistance (DEA) program, covered under Chapter 35, Title 38 of the US Code, can provide educational benefits to dependents of service-members who have been killed or totally disabled in the line of duty. This program, also, is limited to spouses and children of the service-member.
The Serviceman’s Group Life Insurance (SGLI) is completely separate from educational benefits available from the Veterans Affairs department, and doesn’t have any bearing on eligibility for the GI Bill or other educational benefits.