Does my wife need to accompany me to extend my visa at Korat Immigration after her mother's passing?

If you haven't yet used your 30 day extension for the visa exempt entry you should be able to get that without your wife being present

Sorry for the loss of your mother-in-law.

Yes, your wife needs to be with you when you apply for a 60-day extension for visiting Thai family. You always have to bring the "reason" for your extension with you when you apply for it at the local office.

Attached is general information for it. But you need to check with your local office for their requirements. If you haven't applied for 30 days tourism extension, you may required to apply for it first.