Mia madre, invece, non vorrebbe mai un maiale né un topo in casa.

With singular family members in Italian, the possessive often appears without the article:

• mia madre = my mother
• tuo fratello = your brother
• nostra sorella = our sister

This is a very common pattern with close family relationships in the singular.

You usually add the article when:

• the family noun is plural: i miei genitori
• the family noun is modified: la mia cara madre
• the noun is not a close singular family term in the usual sense

So mia madre is the normal choice here.

Invece means something like:

• instead
• on the other hand
• by contrast

In this sentence, it signals a contrast with something said before. For example, if someone else would like an animal in the house, mia madre, invece... means my mother, on the other hand...

It is often set off with commas when it interrupts the sentence like this:

• Mia madre, invece, ...

Because invece is being used as a parenthetical contrast marker, not as a tightly connected part of the main clause.

So:

• Mia madre, invece, non vorrebbe...

feels like:

• My mother, however, would not want...

The commas help show that invece is an inserted contrast word. In everyday writing, punctuation can vary a little, but this comma pattern is very common and natural.

Vorrebbe is the conditional present of volere.

• vuole = she wants
• vorrebbe = she would want

In a negative sentence like this, non vorrebbe often means:

• she would not want
• she wouldn’t want

This can sound more hypothetical, more polite, or more like a personal preference than the more direct non vuole.

Compare:

• Non vuole un topo in casa = She doesn’t want a mouse in the house
• Non vorrebbe un topo in casa = She wouldn’t want a mouse in the house

So vorrebbe fits the idea of a general preference or hypothetical reaction.

Non ... mai means never.

So:

• non vorrebbe mai = she would never want

Even though mai by itself often means ever, when it appears with non, the meaning becomes never.

Examples:

• Lo fai mai? = Do you ever do it?
• Non lo faccio mai. = I never do it.

In your sentence:

• non vorrebbe mai un maiale... = she would never want a pig...

A learner often expects a full né ... né ... structure, and that is possible:

• non vorrebbe mai né un maiale né un topo in casa

But after a negative verb, Italian also very naturally uses:

• un maiale né un topo

So this sentence:

• non vorrebbe mai un maiale né un topo in casa

means:

• she would never want a pig or a mouse in the house
• more literally, ... neither a pig nor a mouse ...

In other words, the first item can appear without né because the negation is already established by non.

Because each noun is being presented as a separate possible animal:

• un maiale = a pig
• un topo = a mouse

Repeating the article is normal and natural in Italian here. It helps keep the coordination clear.

So:

• un maiale né un topo

is like saying:

• a pig nor a mouse

within the larger negative structure.

In casa is a very common Italian expression meaning:

• at home
• in the house
• in the home

Italian often uses in casa without an article in this idiomatic sense.

Compare:

• Sono in casa = I’m at home
• Restiamo in casa = We’re staying at home

If you wanted to refer to a specific house more literally, other forms can appear, such as:

• nella casa
• dentro la casa

But in casa is the normal phrase here.

With a conjugated verb, mai commonly comes after the verb:

• non vorrebbe mai
• non mangia mai
• non esco mai

That is the standard position for never in many simple sentences.

So the order:

• non + verb + mai

is very common and should feel natural to learners.

Yes, it can, especially in less formal writing. The meaning stays the same.

However, with commas:

• Mia madre, invece, non vorrebbe mai...

the contrast feels a bit more clearly marked, like my mother, however...

Without commas:

• Mia madre invece non vorrebbe mai...

it is still perfectly understandable and often heard or seen in everyday language.

Yes, mai adds emphasis.

Compare:

• non vorrebbe un maiale né un topo in casa = she wouldn’t want a pig or a mouse in the house
• non vorrebbe mai un maiale né un topo in casa = she would never want a pig or a mouse in the house

So mai makes the refusal sound more absolute.

Yes. Italian allows some flexibility in word order.

For example, you could also say:

• Mia madre, invece, non vorrebbe mai in casa un maiale né un topo.

That is grammatical, but the original version is smoother and more neutral:

• Mia madre, invece, non vorrebbe mai un maiale né un topo in casa.

Placing in casa at the end is very natural because it neatly gives the setting after the animals are mentioned.