Nie mam z kim zostawić dzieci, więc zabiorę je ze sobą do lekarki.

Because z kim is the instrumental form after the preposition z meaning with.

Literally, Nie mam z kim zostawić dzieci is something like I don’t have with whom to leave the children.

• kto = who
• kim = whom / with whom / by whom, depending on context
• z kim = with whom

This is a very common Polish pattern:

• Nie mam z kim porozmawiać. = I have no one to talk to.
• Nie mam z kim pójść. = I have no one to go with.

So here, the idea is: there is nobody with whom I can leave the children.

Polish often uses mieć (to have) where English uses there is / there are.

So:

• Nie mam z kim zostawić dzieci
  literally = I don’t have with whom to leave the children
• natural English = I have no one to leave the children with

This is very normal Polish wording. English and Polish just structure this idea differently.

Zostawić means to leave, to leave behind, or in this context to leave someone in someone else’s care.

So zostawić dzieci means:

• to leave the children
• more naturally here: to leave the children with someone

In this sentence, it does not mean abandoning them. It means arranging for someone else to look after them.

Because zostawić is perfective, and Polish commonly uses the perfective infinitive after expressions like this when talking about a single completed action.

• zostawiać = imperfective, ongoing/repeated to be leaving / to leave regularly
• zostawić = perfective, one complete act to leave

Here the speaker means one specific act: I have no one to leave the children with on this occasion.

Similarly:

• Nie mam gdzie zaparkować. = I have nowhere to park.
• Nie mam kiedy zadzwonić. = I have no time to call.

The infinitive often points to a single practical action to be completed.

Because dzieci is the accusative plural here, functioning as the direct object of zostawić and later referring to the same children in zabiorę je.

The singular is:

• dziecko = child

The plural is:

• dzieci = children

In this sentence:

• zostawić kogo? co? → dzieci

So dzieci is the object: the speaker wants to leave the children with someone.

Więc means so, therefore, or thus.

The sentence has two parts:

• Nie mam z kim zostawić dzieci
• więc zabiorę je ze sobą do lekarki

So the logic is:

I have no one to leave the children with, so I’ll take them with me to the doctor.

The comma is standard because więc connects two clauses.

Zabiorę is the 1st person singular future form of zabrać, a perfective verb meaning to take, often in the sense of take along, take away, or bring with you depending on context.

Here:

• zabiorę = I will take
• more naturally here: I’ll take them along

So:

• zabiorę je = I’ll take them

Because zabrać is perfective, its present-looking forms have future meaning:

• zabiorę = I will take

Je is the accusative plural pronoun here, meaning them. It refers back to dzieci.

So:

• dzieci = the children
• je = them

That gives:

• zabiorę je = I’ll take them

Polish often uses object pronouns very explicitly where English might do the same, but the important thing is that je is the direct object of zabiorę.

No, they do different jobs.

• je = them → the direct object
• ze sobą = with me → an additional phrase showing accompaniment

So:

• zabiorę je = I’ll take them
• zabiorę je ze sobą = I’ll take them with me

This is very natural Polish. The phrase zabrać kogoś/coś ze sobą is a common pattern meaning to take someone/something with oneself.

Polish often uses ze instead of z for easier pronunciation, especially before certain consonant clusters.

So:

• z sobą would be awkward to say
• ze sobą sounds smoother

This is a normal phonetic variant:

• z mną
• ze sobą
• ze szkoły

Also, sobą is the instrumental form of siebie (oneself), so ze sobą literally means with oneself, and in context here: with me.

Because the preposition do requires the genitive case.

The base noun is:

• lekarka = female doctor

Its genitive singular is:

• lekarki

So:

• do lekarki = to the female doctor

This usually means going to see the doctor, often to her office or appointment.

Compare:

• do lekarza = to the male doctor
• do dentysty = to the dentist
• do szkoły = to school

Yes. Lekarka is specifically a female doctor, and it is a normal modern word in Polish.

Compare:

• lekarz = doctor, traditionally masculine form
• lekarka = female doctor

In many situations, Polish speakers do use the feminine professional noun when the doctor is a woman. So do lekarki clearly tells you the doctor is female.

Yes. Polish word order is flexible, although some versions sound more neutral than others.

The original:

• Nie mam z kim zostawić dzieci, więc zabiorę je ze sobą do lekarki.

This is natural and clear.

Possible variations:

• Nie mam z kim zostawić dzieci, więc zabiorę je do lekarki ze sobą.
• Więc zabiorę je ze sobą do lekarki, bo nie mam z kim zostawić dzieci.

But the original order is good because it presents the problem first and then the solution.

Also, putting ze sobą before do lekarki often sounds slightly more natural, because zabrać kogoś ze sobą is such a common unit.

Yes, and many learners notice that possibility.

• Nie mam komu zostawić dzieci = literally I don’t have anyone to whom I can leave the children
• Nie mam z kim zostawić dzieci = literally I don’t have anyone with whom to leave the children

In real usage, these can be very close in meaning. The version with komu focuses more directly on a person to entrust the children to. The version with z kim is also idiomatic and emphasizes the practical arrangement of leaving them with someone.

So the sentence you were given is natural, but nie mam komu zostawić dzieci is also something you may hear.