Mi madre peruana lleva un chaleco reflectante.

Because mi without an accent is the possessive adjective meaning my.

• mi madre = my mother

With an accent, mí is a pronoun meaning me after a preposition:

• para mí = for me
• de mí = about me / of me

So in this sentence, mi is correct because it is describing madre.

Spanish often does not need a separate word for is when using a normal verb.

Here, the main verb is lleva, which means something like wears / is wearing / carries, depending on context. So:

• Mi madre peruana lleva un chaleco reflectante.
• literally: My Peruvian mother wears/is wearing a reflective vest.

English often uses is wearing, but Spanish can simply use the present tense lleva.

In Spanish, nationality adjectives usually come after the noun.

• madre peruana = Peruvian mother
• amigo mexicano = Mexican friend
• comida colombiana = Colombian food

So mi madre peruana is the normal word order.

If you put peruana before madre, it would sound unusual, literary, or emphatic in most contexts.

Because peruana agrees in gender with madre, which is feminine.

• madre peruana = feminine
• padre peruano = masculine

Many Spanish adjectives change form to match masculine/feminine nouns:

• mexicano / mexicana
• argentino / argentina
• peruano / peruana

Since madre is feminine, the adjective must also be feminine: peruana.

Because the article agrees with the noun chaleco, not with the person wearing it.

• chaleco is a masculine noun
• so it takes un

That is why we say:

• un chaleco reflectante

Even if the person is female, the clothing noun keeps its own gender:

• Mi madre lleva un chaleco
• Mi hermana lleva un abrigo
• Mi tía lleva una chaqueta

Because reflectante is an adjective that usually does not change for masculine and feminine.

Many adjectives ending in -e or a consonant stay the same:

• un chaleco reflectante
• una chaqueta reflectante

So reflectante works for both masculine and feminine nouns. It only changes for number:

• un chaleco reflectante
• dos chalecos reflectantes

Here, lleva means wears or is wearing.

The verb llevar has several meanings, including:

• to carry
• to take
• to wear

In clothing contexts, llevar commonly means to wear:

• Lleva un sombrero. = He/She is wearing a hat.
• Llevo botas. = I’m wearing boots.

So in this sentence, context tells you it means is wearing, not carries.

Yes, you could, but it is not exactly the same in feel.

• lleva un chaleco reflectante = is wearing a reflective vest
• usa un chaleco reflectante = uses / wears a reflective vest

Llevar is very common when talking about what someone has on their body at that moment.
Usar can also work, but it may sound a little more general, like the person habitually uses that item.

For describing what someone is wearing right now, llevar is often the most natural choice.

Because Spanish usually drops subject pronouns when the verb already makes the subject clear.

• lleva can mean he/she/it wears
• the sentence already has the subject: Mi madre peruana

So ella is unnecessary:

• Mi madre peruana lleva un chaleco reflectante.

You could say:

• Ella lleva un chaleco reflectante.

But in this sentence, repeating the subject would usually be less natural unless you want emphasis or contrast.

Here, peruana is an adjective modifying madre:

• madre peruana = Peruvian mother

But peruana can also be a noun meaning a Peruvian woman:

• Ella es peruana. = She is Peruvian.
• La peruana habla español. = The Peruvian woman speaks Spanish.

So the same word can function as either an adjective or a noun depending on the sentence.

In Spanish, most descriptive adjectives normally come after the noun.

• un chaleco reflectante
• una casa grande
• un coche rojo

So chaleco reflectante is the normal order.

Putting an adjective before the noun is sometimes possible in Spanish, but it often changes the tone, adds emphasis, or sounds literary. For this kind of practical description, noun + adjective is the standard pattern.

You would make the noun, article, and adjective plural where needed:

• Mis madres peruanas llevan chalecos reflectantes.

Changes:

• mi → mis
• madre → madres
• peruana → peruanas
• lleva → llevan
• un chaleco reflectante → chalecos reflectantes

If you wanted to keep the article, you could also say:

• Mis madres peruanas llevan unos chalecos reflectantes.

But in many cases, Spanish often leaves out the indefinite article in plurals.

The original sentence already can mean that, but if you want to make the right now meaning clearer, you have a few options:

• Mi madre peruana lleva un chaleco reflectante.
• Mi madre peruana está usando un chaleco reflectante.
• Mi madre peruana tiene puesto un chaleco reflectante.

Notes:

• lleva is very natural and common
• está usando emphasizes the ongoing action a bit more
• tiene puesto strongly emphasizes that she has it on

In everyday Spanish, lleva is often enough.