If you enjoy timesharing, you need to spend time researching which timeshare system is suitable for your needs. You may very well find that Diamond timeshare system is not what you want to own. If so, make sure you decline the inheritance. However, if you like what you learn about Diamond vs. other timeshare systems, then you need to figure out if it is a financial burden that you want to afford.
I am friends with a couple in their 70s who owns only several relatively high MF resorts under the Vistana system (Princeville, Kaanapali, Westin Mission Hills) and Marriott (Ko Olina). They own several weeks at each of the resort because when they travel, they travel with some or all of their children, children's spouses and grand children. I cannot imagine what their MFs are but several of their children and spouses have already told them which of their timeshare that they want for inheritance. Because they have 8 children, and some are doing financially better than others, they are not worried about what will happen to their timeshare one day when they no longer have use for them or when they die. This couple bought their timeshares from the developers and scoffed when I told him to ask one of his sons-in-law to buy Westin Princeville in the resale market as he has been pestering them about letting him have their timeshare now.
Most timeshares cost alot less in the resale market. So you may find that picking up something in the resale market is less of a financial burden than taking over from your parents' DRI timeshare in the future.