Well, regardless to of the meaning of the sentence, I know that the word "general" is an adjective and the word "driving" is a noun which is a gerund, so if I write it in this way "My mother's driving is general", will it be is it grammatically correct?
Even if it has no meaning since though I knew from you told me that there is nothing called no such thing as "general driving", but is it grammatically correct no question mark here OR or do I have to change it into "My mother's driving is generally"?
1. "General" is both a noun and an adjective. In your original sentence, it's an adjective.
2. What possible use is knowing whether the sentence is grammatically correct if it's meaningless? That's a pointless question.
3. "My mother's driving is generally" is, if anything, worse than the original. "Generally" is an adverb meaning "in general". You could say "My mother's driving is generally terrible", meaning "Most of the time, she drives really badly".
I'm not sure what your problem is here. There are hundreds of adjectives that don't collocate with "My mother's driving is ...". You just happen to have found one of them.
Note my corrections in the quote box. Please take more care with your punctuation and spacing around it. Don't put a space after opening quotation marks. Don't put a space before closing quotation marks.