Noun endings are probably one of the hardest parts when starting to learn Latin, especially since there are a few declensions and have different ending. Eventually you will know them and it will make parsing a sentence much easier.
A decent resource would potentially be looking the word up on a site like Wiktionary. It provides you will the nouns in their different forms. Like for mater: https://en.wiktionary.org/wiki/mater#Latin. There is a table that gives you the noun in all its cases.
Think of māter = SHE, the mother (only used as a subject: SHE, the mother, visits us), and of mātrem = HER, the mother (used as an object: We visit HER, the mother).
The adjective "our" has to be the same CASE (= subject/object) as the noun it describes, and the same NUMBER ( = sing/plur), and the same GENDER ( = masc/fem/neuter).
SO, māter nostra versus mātrem nostram .
Notice that both "mother" and "our" end in an ending that uses the letter m . All masculine and feminine nouns/adjectives use a "vowel plus m" letter, to indicate the accusative singular ending:
1st declension: am
2nd declension: um
3rd declension: em
(The 2nd declension neuters also use the ending um , for both nominative and accusative singular; for neuters, nominative and accusative cases are always identical.
The 3rd declension neuters, and 4th declension neuters, are the only singular accusatives that don't use m , to form the accusative singular. Examples are iter, itineris , n., "journey," whose accusative singular is also iter ; and genu, genūs , n., "knee," whose accusative singular is also genu . )
Domi = (locative) at home. So, this is not a house with a possessive, but it plays an adverbial role (adverbial phrase of place).
Matrem nostram = accusative. Nostram match with matter in case and in gender. It's our mother.
As we visit our mother at home, we guess we go in our mother's house. "At home" refers logically here to "her home". As we can't visit someone else (=going in order to see someone) in our own home.
It's an adjective; remember that adjectives describe the noun they modify.
We'd say "the angry mother": mātrem īrātam , right?
What makes this seem 'weird' is that it's a possessive adjective; so, think of the BASE or STEM as indicating "the group":
it's the _nostr- _ that carries the meaning "our, belonging to us";
and the ending we put on nostr- "attaches" the adjective to the item (in this case, the mother) that we 'possess':
"our mother", accus. fem. sing., so: mātrem nostram
Please let me know if that's in any way unclear.
(My mother: mātrem meam. and My father: patrem meum )