Learn Hardcore Croatian: Roditelji joj ne žele dopustiti kasni izlazak, jer misle da veza s novim dečkom još nije stabilna. - Her parents do not want to allow her to go out late, because they think that the relationship with her new boyfriend is not yet stable.

joj is a clitic (short unstressed pronoun) and must stand very close to the beginning of the clause, after the first stressed element (here: Roditelji).
That is why you get Roditelji joj ne žele…, not Roditelji ne žele joj…. The latter sounds wrong to native speakers.

Why do we have ne žele dopustiti and not just one verb?

The combination žele dopustiti corresponds to English want to allow:

žele = they want
dopustiti = to allow, to permit (infinitive)

So ne žele dopustiti = they don’t want to allow.

Croatian often uses:

a finite verb expressing volition/ability (e.g. želim, moram, mogu)
an infinitive expressing the main action (e.g. raditi, dopustiti, ići)

Examples:

Ne želim ići. – I don’t want to go.
Ne smijem pušiti. – I must not smoke / I am not allowed to smoke.

Here, the main act is dopustiti (to allow), and žele just expresses their will about that act.

Why is it kasni izlazak and not kasno izlazak or kasni izlaz?

This is about adjective vs adverb, and the correct noun:

izlazak vs izlaz
- izlazak = going out / outing (the act of going out socially)
- izlaz = exit (door, way out of a building)

Here we mean a late outing, not a physical exit, so izlazak is correct.

kasni vs kasno
- kasni is an adjective (“late”) and must agree with the noun:
  - kasni izlazak – late outing
- kasno is an adverb (“late” as in to come late), it normally modifies a verb:
  - doći kasno – to come late

Since izlazak is a noun, we need an adjective, so kasni izlazak is correct, not kasno izlazak.

What case is joj, and why is the dative used?

Joj is dative singular feminine, from ona (she).

The dative is used for:

indirect objects (to/for someone)
people who benefit from or are affected by an action

In English you would say:

Her parents don’t want to allow *her a late night out.*

Croatian expresses that to her idea by using the dative:

Roditelji joj ne žele dopustiti kasni izlazak.
literally: Parents to‑her don’t want to allow a late outing.

No preposition is needed; the case itself (dative) carries the meaning of to her.

Why is it s novim dečkom and not sa novim dečkom or some other form?

S (or sa) is a preposition that usually corresponds to with.

s/sa + instrumental means with someone/something.

Here we have:

novim – instrumental singular masculine of novi (new)
dečkom – instrumental singular of dečko (boyfriend, boy)

So s novim dečkom = with (her) new boyfriend.

About s vs sa:

Before many consonants, s is fine: s njim, s tobom, s bratom, s novim dečkom.
sa is used:
- to avoid difficult consonant clusters (s stolom → sa stolom), or
- just by stylistic preference in some phrases.

Here, s novim dečkom is perfectly natural. Sa novim dečkom is also possible and not wrong, but less needed phonetically.

Why is it veza s novim dečkom and not something else like veza s novog dečka?

Veza s novim dečkom uses the instrumental to show a relationship with someone:

veza – relationship, (romantic) relationship
s (sa)
- instrumental = with
novim dečkom – instrumental singular (with the new boyfriend)

So literally: relationship with (the) new boyfriend.

Veza s novog dečka would be:

novog dečka = genitive singular, not instrumental
This would sound wrong and ungrammatical in standard Croatian for this meaning. You need the instrumental after s/sa to mean with someone.

Why does it say jer misle da…? Is da necessary after misliti?

Jer introduces a reason clause: because.

jer misle da… = because they think that…

The da here works like English that introducing a subordinate clause:

misliti da = to think that

You can sometimes drop da in very informal or colloquial speech, especially with verbs like reći (to say), misliti (to think), znati (to know), but:

misliti da
- clause is the standard, neutral way.
misliti followed directly by a finite clause without da can sound colloquial or incomplete.

So jer misle da veza s novim dečkom još nije stabilna is the natural, standard structure.

Why is it veza … nije stabilna and not nije stabilan or stabilno?

This is grammatical agreement between the noun and the adjective:

veza is feminine singular.
The adjective stabilan (stable) must agree with veza, so in the feminine singular it becomes stabilna.

Forms of stabilan:

masculine singular: stabilan
feminine singular: stabilna
neuter singular: stabilno

Since veza is feminine, the correct form is stabilna:

veza nije stabilna – the relationship is not stable.

Stabilan would match a masculine noun, and stabilno would match a neuter noun or function as an adverb.

What is the role of još in još nije stabilna, and could the word order be nije još stabilna?

Još means still, yet.

još nije stabilna = is not stable yet / is still not stable.

About word order:

još nije stabilna is the most neutral word order here.
nije još stabilna is also grammatically correct. It can sound slightly more contrastive or emphatic, like stressing the not yet part.

Important point: ne must come directly before the verb:

ne + jesti, ne + želi, ne + misle
So you cannot say još ne stabilna; it must be još nije stabilna (ne + je → nije).

Why is it ne žele dopustiti and not something like ne dopuste kasni izlazak?

There is a difference in meaning:

ne žele dopustiti kasni izlazak
= they don’t want to allow a late outing
(it talks about their wish/intention)
ne dopuste kasni izlazak
= they don’t allow a late outing (or won’t allow, depending on context)
(focuses on the act of not allowing, not on what they want)

The original sentence describes their attitude / intention (they are unwilling to allow it), so ne žele dopustiti is the natural choice. Using only ne dopuste would shift the meaning.

Could the word order be Roditelji ne žele joj dopustiti kasni izlazak? Why is joj placed where it is?

No, Roditelji ne žele joj dopustiti… sounds wrong in standard Croatian.

Reason:

Joj is a clitic pronoun, and Croatian has strict rules about clitic placement.
In a main clause, clitics usually go in “second position”: after the first stressed word or phrase of the clause.

In your sentence:

First stressed element: Roditelji
Then the clitic: joj
Then the rest: ne žele dopustiti…

So:

Roditelji joj ne žele dopustiti kasni izlazak… ✅ natural
Roditelji ne žele joj dopustiti kasni izlazak… ❌ wrong ordering of the clitic

Why is there a comma before jer?

The comma marks the boundary between the main clause and the subordinate reason clause introduced by jer:

Main clause: Roditelji joj ne žele dopustiti kasni izlazak
Reason clause: jer misle da veza s novim dečkom još nije stabilna.

In standard Croatian orthography:

A comma is normally used before jer when it introduces a clause meaning because.

So the comma is expected:
…, jer misle da…

Why is izlazak used (a noun) instead of a verb phrase like da izađe kasno?

Croatian, like English, can talk about actions using nouns (nominalizations) or verb clauses.

Here:

kasni izlazak = a late outing / staying out late (noun phrase)
Possible verb alternative:
- Roditelji joj ne žele dopustiti da kasno izađe…
  = They don’t want to allow her to go out late…

Both are grammatically fine, but they have slightly different styles:

kasni izlazak (noun) sounds compact and neutral; very common in speech and writing.
da kasno izađe (verb clause) puts more focus on the action of going out late.

The sentence with kasni izlazak is totally natural and idiomatic.