Moje dcera je ve škole, ale můj syn je doma.

Because the possessive pronoun my must agree with the noun being possessed.

• dcera (daughter) is a feminine noun, so you use moje
• syn (son) is a masculine noun, so you use můj

So:

• moje dcera = my daughter
• můj syn = my son

In Czech, this kind of agreement is very important.

Both v and ve mean in or at, but ve is used when it sounds easier to pronounce before certain consonants or consonant clusters.

Since škole begins with šk-, Czech normally uses ve škole rather than v škole.

So:

• ve škole = at school / in school

This is mostly about pronunciation and natural flow.

Because the preposition v / ve requires the locative case when it means location.

The base form is:

• škola = school

After ve, it changes to the locative form:

• ve škole = at school

So this is a case change, not a different word.

Doma is a very common Czech adverb meaning at home.

So:

• je doma = is at home

Czech often uses doma instead of a preposition + noun phrase here.
You can also encounter forms related to dům (house/home), but doma is the normal everyday way to say at home.

Je is the 3rd person singular form of the verb být (to be).

So:

• dcera je ve škole = the daughter is at school
• syn je doma = the son is at home

It corresponds to English is.

Ale means but.

It connects two contrasting ideas:

• Moje dcera je ve škole = My daughter is at school
• ale můj syn je doma = but my son is at home

So it works just like English but in this sentence.

Not always, but in this sentence it is natural because the speaker is clearly contrasting my daughter with my son.

You could sometimes omit a possessive if the meaning is obvious from context, but repeating it makes the contrast clearer:

• Moje dcera je ve škole, ale můj syn je doma.

That sounds complete and natural.

Not as strictly as in English.

The sentence uses a very neutral word order:

• Moje dcera je ve škole, ale můj syn je doma.

Czech word order is more flexible because endings carry a lot of grammatical information. Different word orders can change emphasis, but this version is the most straightforward and natural for a learner.

Můj is pronounced roughly like mooy in one syllable.

A few useful notes:

• ů sounds like a long oo
• j in Czech is pronounced like English y

So můj is approximately mooy.

Škole is pronounced approximately SHKO-leh.

Helpful parts:

• š = sh
• ko = like ko
• le = leh

So ve škole sounds roughly like veh SHKO-leh.

It can mean either, depending on context.

In this sentence, ve škole most naturally means:

• at school

But Czech v / ve + locative often covers meanings that English expresses as either in or at.

So ve škole can be understood as in the school or at school, depending on what the speaker means.