The parsing of these language bits comes together oddly for the female voice, at times. I understood the slowed version fine "c'est - ma - mère", but the normal speed version sounded slurred, almost with an 'm' sound in it. "C'est lemmère". I don't seem to have any of this problem with the male voice. :\
"Ce" and "cette" are 2 of the 4 demonstrative adjectives modifying nouns:
Ce chien (masculine singular, before a consonant sound)
Cet homme / cet enfant (masculine singular, before a vowel sound)
Cette femme (feminine singular)
Ces enfants (plural)
"Ce" is also a pronoun you can use in "c'est" or "ce sont".
Read again what I said earlier: "cette" is a determiner (a demonstrative adjective) which must be immediately followed by a noun.
"Ma" is also a determiner (a possessive adjective) and you cannot use 2 determiners one after another. You would not say "this my mother" without a verb in English, so you cannot have "cette ma mère" in French either.
"She is my mother" is "c'est ma mère", where "c'" (a pronoun) replaces "elle".
This is how you can use "cette": "Cette femme est ma mère" = This woman is my mother.
For foreigners learning French, we would literally translate "C'est ma mère" as "It is my mother". If the answer is meant to be "She is my mother", then it should be "Elle ma mère".
"C'est ma mère/She is my mother" might (or not) be acceptable by native French speakers. But for us foreigners, we need to learn it the precise and grammatically correct way to AVOID any confusion and inconvenience.
So, in this case, it either needs to be "C'est ma mère/It is my mother" or "Elle ma mère/She is my mother".
C'est ma mère = She is my mother (WRONG) C'est ma mère = It is my mother (CORRECT) Elle ma mère = She is my mother (CORRECT)
"Elle est ma mère" is not what French people use, unless they want to produce a stylistic, emphatic effect.
The general rule is that when "elle est" is followed by a modified noun (a noun preceded by a determiner), you change it to "c'est". The same applies to "il est" and in the plural, "ils/elles sont" + modified noun has to change to "ce sont".
"C'est ma mère" is the translation for "It/This/That/She is my mother".