Da nisam morala u banku zbog kredita, ranije bih stigla veterinaru.

Yes, da very often means that, but it also has other uses.

Here, da introduces a counterfactual conditional clause:
Da nisam morala... = If I hadn’t had to...

So in this sentence, da is not functioning as that. It is part of a common Croatian pattern for unreal past situations:

Da + past form, ... bih + past participle

Example pattern:

• Da nisam došla, ne bih te vidjela.
• If I hadn’t come, I wouldn’t have seen you.

This is very common in spoken and written Croatian.

Because Croatian usually forms this kind of past unreal condition with:

• da + perfect-like past form in the if-clause
• bih/bi/bismo/biste/bi + past participle in the main clause

So:

• Da nisam morala u banku...
• ... ranije bih stigla veterinaru.

Literally, the first part is structured like I didn’t have to, but in context with da, it means if I hadn’t had to.

That may feel unusual to an English speaker, because English uses hadn’t had to, while Croatian uses its own pattern.

Because the speaker is understood to be female.

In Croatian past forms and conditional participles agree with the subject’s gender and number:

• morala, stigla = feminine singular
• morao, stigao = masculine singular
• morali, stigli = masculine/mixed plural
• morale, stigle = feminine plural

So this sentence is something a woman would say.

A man would say:

Da nisam morao u banku zbog kredita, ranije bih stigao veterinaru.

Because Croatian often drops subject pronouns when they are not needed.

The verb forms already tell you enough, and here the participles also show gender:

• nisam morala
• bih stigla

That makes ja unnecessary unless you want extra emphasis.

So:

• Da nisam morala... = natural
• Da ja nisam morala... = possible, but more emphatic

Croatian does this much more than English.

Because u can take two different cases depending on meaning:

• u + accusative = movement into/to
• u + locative = location in

So:

• u banku = to the bank
• u banci = in the bank

In your sentence, the speaker had to go to the bank, so movement is involved, which is why Croatian uses accusative:

u banku

Zbog requires the genitive case.

So:

• kredit = nominative
• kredita = genitive

That is why the phrase is:

zbog kredita = because of the loan

This is a fixed preposition + case combination, and it is worth memorizing:

• zbog + genitive

Other examples:

• zbog posla = because of work
• zbog kiše = because of the rain
• zbog djece = because of the children

Veterinaru is dative singular.

Here it means something like to the vet.

With verbs of arrival or movement toward a person, Croatian can use the dative without a preposition:

• ići liječniku = to go to the doctor
• doći zubaru = to come to the dentist
• stići veterinaru = to arrive at/to the vet

So veterinaru is dative, and it is being used as the destination.

That is a very good question, because both patterns can appear, but they are not exactly the same.

veterinaru (dative)

This focuses on the person as the destination:

• stigla veterinaru
• otišla liječniku

kod veterinara

This literally means at the vet’s place / to the vet’s office It is also very common:

• otišla sam kod veterinara
• bila sam kod veterinara

So in this sentence, veterinaru is grammatical and natural, especially with verbs like stići, doći, ići.
But kod veterinara would also be very understandable in many contexts.

Very roughly:

• veterinaru = to the vet
• kod veterinara = to/at the vet’s office

Ranije means earlier.

It is the comparative adverb related to rano (early):

• rano = early
• ranije = earlier

So:

ranije bih stigla = I would have arrived earlier

Depending on context, English might translate it as earlier or sometimes sooner, but earlier is the most direct match here.

Because the main clause expresses a hypothetical result, not a real past event.

• stigla sam = I arrived
• bih stigla = I would arrive / I would have arrived

In this sentence, the speaker is talking about something that did not actually happen:

If I hadn’t had to go to the bank because of the loan, I would have arrived earlier at the vet’s.

That is why Croatian uses the conditional:

• bih stigla

Yes. In this context, bih stigla is understood as a past unreal result.

Croatian does not always match English tense structure word-for-word. The combination of:

• Da nisam morala...
• ... bih stigla

clearly signals a counterfactual past meaning.

So although the Croatian form looks shorter than English would have arrived, the meaning is the same here.

Yes. Croatian word order is fairly flexible, and this sentence could be rearranged for emphasis.

For example:

• Da nisam morala u banku zbog kredita, ranije bih stigla veterinaru.
• Da nisam morala u banku zbog kredita, bih stigla ranije veterinaru. → not natural, because bih should not be stranded like this
• Da nisam morala u banku zbog kredita, stigla bih ranije veterinaru.
• Da nisam morala zbog kredita u banku, ranije bih stigla veterinaru.

The most natural alternatives are usually:

• ... ranije bih stigla veterinaru
• ... stigla bih ranije veterinaru

Both are fine. Word order affects emphasis more than basic meaning.

It is grammatical and understandable, but some speakers might more naturally say:

• ranije bih stigla kod veterinara
• ranije bih stigla veterinaru
• ranije bih došla veterinaru
• ranije bih stigla do veterinara in some contexts, though this can sound more like physically reaching the place

The version with veterinaru is perfectly possible, especially by analogy with expressions like:

• ići liječniku
• doći zubaru

But in everyday speech, kod veterinara is also extremely common.

So this is not wrong at all; it is just good to know that Croatian often offers more than one idiomatic way to say to the vet.

Only the gender-marked participles would change:

Da nisam morao u banku zbog kredita, ranije bih stigao veterinaru.

Changes:

• morala → morao
• stigla → stigao

Everything else stays the same.

The main verbs are:

• morala → morati = to have to, must
• stigla → stići = to arrive
• nisam → from biti = to be, used here as an auxiliary

So the sentence is built from:

• morati
• stići
• auxiliary biti

This is useful because you usually look up Croatian verbs in the dictionary by the infinitive:

• morati
• stići