Is it possible for genetic testing determine if this disease was inherited from mother or father?

Yes: This is now routine. An autosomal recessive disease occurs when both parents are carriers, and the mutation contributed by each can be identified. An autosomal dominant with variable expression can be traced to the affected parent, or it can be determined that the child has a new mutation that does not affect either parent.

Depends on the disea: Some afflictions are not gene related while the inheritance pattern of others can be traced. Some well known genetic conditions arise as a new mutation in the majority of affected persons. If both parents are living & available for study, many inherited disorders can be tracked. A consultation with a geneticist, often affiliated with a regional children's hospital would be a good starting point.