Could you please help me translate "mother's son" into Latin?
From my understanding it is "filius matris" but I am not 100% sure.
Yes, you can be 100% sure.
Just watch out, though; "His mother's son" will be Filius matris suae, because suae agrees in gender number and case with (genitive, feminine, singular) matris.
"Her Mother's son" is also Filius Matris suae: Think of it as modern 'their Mother's son' even when 'their' means only one person. (But it is ambiguous)