Thanks for the query to H.C.M. Forum.
Since these movements are at rest and involuntary so call as rest tremors.
The characteristic features of these movements is maximal at rest while less prominent with activities.
As you stated that while hand is on the table tremors occurs, so also when fingers at steering wheel.
You stated that these movements increase when sugary products consumed more.
Sugar ( carbohydrate
) actually decreases dopamine
secretion hence there develops more tremors i.e. less dopamine more tremors.
In my opinion please consult a neurologist
and get his opinion and treatment .
Possible diagnosis in my point of view may be Parkinsonism Disease.
Good luck for your husband.