Mi hija quiere acariciar al conejo en la granja.

Because after querer (to want), the next verb stays in the infinitive form.

• quiere = she wants
• acariciar = to pet / to stroke

So quiere acariciar literally means wants to pet.

This is the same pattern as in English:

• She wants to eat
• Ella quiere comer

You do not conjugate the second verb after querer unless you start a new clause.

Querer is the infinitive, meaning to want. In the sentence, the verb has to agree with mi hija, which is she.

So:

• querer = to want
• quiere = she wants

This is the present tense of querer:

• yo quiero
• tú quieres
• él/ella/usted quiere
• nosotros queremos
• vosotros queréis
• ellos/ellas/ustedes quieren

Notice that querer is a stem-changing verb:

• e → ie in most forms
• but not in nosotros and vosotros

In normal Spanish, possessive adjectives like mi usually go before the noun:

• mi hija = my daughter

You do not say la mi hija in standard modern Spanish.

You can say hija mía, but that has a different feel. It is usually:

• more emotional
• more emphatic
• sometimes used when directly addressing someone

Examples:

• Mi hija quiere salir. = My daughter wants to go out.
• ¡Hija mía! = My daughter! / Dear daughter!

So in this sentence, mi hija is the normal and natural choice.

Because Spanish often uses the personal a before a specific direct object, especially when it refers to a person, and sometimes also to animals when they are viewed as specific or individual.

Here:

• acariciar is the verb
• el conejo is the direct object
• because it is a specific rabbit, Spanish uses a

So:

• a + el = al
• acariciar al conejo = to pet the rabbit

This does not mean the rabbit is the indirect object. It is still the direct object.

Compare:

• Veo al perro. = I see the dog.
• Quiero al perro. = I love the dog.

With animals, the personal a is very common when the animal is specific.

Al is a contraction of a + el.

So:

• a el conejo becomes al conejo

Spanish always contracts a + el into al, except when el is part of a proper name, such as:

• a El Escorial

In your sentence:

• acariciar al conejo = to pet the rabbit

So al is not a separate special word here; it is simply the required contraction.

Yes. Conejo is a masculine noun in Spanish, so it normally takes el in the singular.

• el conejo = the rabbit
• los conejos = the rabbits

If you specifically mean a female rabbit, you could say:

• la coneja

But if you are just talking about a rabbit in general, conejo is often used as the default noun.

Not exactly.

Acariciar means something like:

• to pet
• to stroke
• to caress

It suggests a gentle, affectionate touch.

Tocar just means:

• to touch

So:

• acariciar al conejo = to pet the rabbit
• tocar al conejo = to touch the rabbit

If someone is gently stroking an animal, acariciar is the better word.

Because in Spanish, the infinitive itself already covers the meaning of to + verb.

So:

• acariciar = to pet
• comer = to eat
• ir = to go

That is why:

• quiere acariciar = wants to pet

Spanish does not need a separate word equivalent to English to in this structure.

Usually en la granja can be understood as at the farm or on the farm, depending on context. English chooses between at and on, but Spanish commonly uses en for both kinds of location.

So:

• en la granja = at/on the farm

In this sentence, it most naturally tells you where the action is happening.

Usually it is understood as describing the situation/location of the action:

• My daughter wants to pet the rabbit at the farm

In practice, that also implies the rabbit is there, but grammatically Spanish often leaves this kind of attachment a little flexible, just like English can.

If you wanted to make it more clearly about the rabbit itself, you could rephrase:

• Mi hija quiere acariciar al conejo que está en la granja.
  • My daughter wants to pet the rabbit that is at the farm.

But the original sentence is completely natural.

Yes. Since el conejo is the direct object, you can replace it with lo:

• Mi hija quiere acariciarlo. = My daughter wants to pet it / him.

With a verb like querer + infinitive, the object pronoun can go in two places:

• before the conjugated verb: Mi hija lo quiere acariciar
• attached to the infinitive: Mi hija quiere acariciarlo

Both are correct. The second version is often especially natural.

Because Spanish often leaves out subject pronouns when the verb already makes the subject clear.

• quiere already tells you it is he/she/you formal
• and mi hija explicitly names the subject anyway

So adding ella would usually be unnecessary:

• Mi hija quiere acariciar al conejo en la granja. = natural
• Ella quiere acariciar al conejo en la granja. = possible, but now the subject is just she
• Mi hija, ella quiere... = only in special emphatic contexts

Spanish generally uses subject pronouns less often than English.

Hija is pronounced roughly like EE-ha.

A few useful points:

• the h is silent
• the j has a strong throaty sound in Spain Spanish
• the stress falls on the first syllable: HI-ja

So it is not pronounced like the English h in hill, and the j is not like the English j in jam.