My mother Mary met is pretty nice.

JungKimIs this sentence grammatical?

It makes no sense. The relative pronoun is required, or the extra verb should be removed.

My mother, who Mary met, is pretty nice.
My mother Mary met is pretty nice.

JungKimIs this sentence grammatical?

No, I cannot make sense of it, actually. Does it mean, "My mother met Mary, who is pretty nice"?

(X-posted)

Mister MicawberDoes it mean, "My mother met Mary, who is pretty nice"?

No, it's supposed to mean "My mother, who Mary met, is pretty nice." But somehow there is no commas or the "who" in the book.

JungKimBut somehow there are no commas or the "who" in the book.

The book is wrong.

JungKimNo, it's supposed to mean "My mother, who Mary met, is pretty nice." But somehow there is no commas or the "who" in the book.

They might have made the sentence by analogy with e.g. "The woman Mary met is pretty nice", which is correct. However, it won't work with "My mother" because "My mother" is already fully defined and cannot take another definer.

This one is correct:
The woman (who) Mary met is pretty nice.

If you have a defining relative clause and the relative pronoun is not the subject of the verb, the relative pronoun (and helping verb, if present) is optional.

The relative clause "who Mary met" defines (or identifies) "the woman."

This one is not correct:
My mother Mary met is pretty

AlpheccaStarsThis one is correct:The woman (who) Mary met is pretty nice.

Or 'whom', of course.

Mister MicawberOr 'whom', of course.

Absolutely, if you want to sound like a uber-formal dowager.

AlpheccaStarsf you want to sound like a uber-formal dowager.

But I don't. I sound like a very competent English speaker. My grammar is at least faultless there. Yours could be challenged.

Mister MicawberMy grammar is at least faultless there. Yours could be challenged.

Very true, but the language has been evolving.
Inflected forms of verbs, nouns and pronouns have been disappearing since Old English.