The English sentence doesn't make it clear whether "convincing" is a verb or an adjective. Of course this topic is on verbs, but that English sentence, without a subject for "convincing", looks a lot more like a description.
The same goes for the Hebrew word. משכנע can be an adjective or a verb.
Although I would have thought that if it was being used as a verb, it would say, "My dad is convincing MY MOM," or whoever....?
Would "My dad is persuasive" also be correct?