Kad se vratim kući, djeca mi odmah trče u zagrljaj.

In Croatian, after kad meaning when, a future event is often expressed with the present tense of a perfective verb, not with the future tense.

So:

• Kad se vratim kući = When I come back home
• literally it looks like present tense, but it can refer to a future completed event

Also, this sentence sounds very natural as a habitual statement:

• Whenever I come home, the children immediately run into my arms.

Using Kad ću se vratiti would not work here.

A useful pattern is:

• Kad dođem, nazvat ću te. = When I arrive, I’ll call you.
• Kad završim posao, idem kući. = When I finish work, I’m going home.

So vratim is correct because Croatian often uses the present of a perfective verb in this kind of time clause.

This is about aspect.

Croatian has two main aspects:

• imperfective: ongoing, repeated, or unfinished action
• perfective: completed, single whole action

Here:

• vraćati se / vraćam se = imperfective = to be returning / to return repeatedly
• vratiti se / vratim se = perfective = to return, to come back

In Kad se vratim kući, the idea is when I have returned / when I get back, so the completed event is important. That is why Croatian uses the perfective verb vratiti se.

If you said Kad se vraćam kući, it would suggest something more like:

• When I am on my way home
• or When I usually return home

So the aspect changes the meaning quite a bit.

Because vratiti se is the normal verb for to return / to come back.

Compare:

• vratiti nešto = to return something
• vratiti se = to return oneself / to come back

So:

• Vratim knjigu. = I return the book.
• Vratim se kući. = I return home.

In many Croatian verbs, se is part of the standard form of the verb and is not translated word-for-word into English. Here it is necessary.

Kući is a very common special form meaning home in the sense of to home / homeward.

So:

• idem kući = I’m going home
• vraćam se kući = I’m returning home

This is more idiomatic than u kuću, which usually means into the house in a more literal, physical sense.

Compare:

• Idem kući. = I’m going home.
• Idem u kuću. = I’m going into the house.

Also compare:

• kod kuće = at home
• iz kuće = out of the house / from home

So kući is simply the normal, idiomatic way to say home after verbs of motion.

Yes, djeca can look confusing at first.

It means children and takes plural agreement:

• Djeca trče. = The children are running.
• Djeca su gladna. = The children are hungry.

It is the irregular plural corresponding to dijete = child.

So even though the form may not look like a typical plural to an English speaker, it behaves as a plural noun in sentences like this.

Here mi is the unstressed dative form meaning to me.

So:

• djeca mi trče u zagrljaj literally = the children run into an embrace to me
• more natural English = the children run into my arms or the children run to hug me

This mi often expresses the person affected or involved, and English often translates it more naturally rather than word-for-word.

Compare:

• Sin mi spava. = literally My son is sleeping on me/to me, but naturally My son is asleep or My son is sleeping with a nuance of personal involvement
• Djeca mi rastu. = My children are growing up

So mi here gives the sense to me / into my arms.

You could say moja djeca, but it is not exactly the same in tone.

• djeca mi is very natural and often sounds more personal, softer, and idiomatic
• moja djeca is more explicit and can sound more emphatic

Compare:

• Djeca mi odmah trče u zagrljaj. = very natural, warm, everyday Croatian
• Moja djeca odmah trče u zagrljaj. = possible, but the possession is stressed more directly

Croatian often uses the dative clitic like mi, ti, mu, joj where English would use my, your, his, her.

Because this is a difference between motion toward something and location in something.

After u:

• accusative = motion into
• locative = location in

So:

• u zagrljaj = into an embrace
• u zagrljaju = in an embrace

Here the children are moving toward the embrace, so accusative is required:

• trče u zagrljaj = they run into an embrace / into my arms

If you said u zagrljaju, it would mean they are already there:

• Djeca su mi u zagrljaju. = The children are in my embrace.

Croatian uses the singular very naturally here.

• u zagrljaj literally means into an embrace
• idiomatically, it often corresponds to English into my arms or for a hug

The singular noun expresses the whole act/state of embracing, not one individual countable hug.

So even if English might prefer arms or sometimes a hug, Croatian very naturally says:

• trčati nekome u zagrljaj = to run into someone’s arms

This is a fixed and common expression.

Croatian usually leaves out subject pronouns when they are clear from the verb ending.

• vratim already tells you the subject is I
• so ja is unnecessary unless you want emphasis or contrast

Compare:

• Kad se vratim kući... = neutral, natural
• Kad se ja vratim kući... = when I come home... with extra emphasis, maybe contrasting with someone else

This is very common in Croatian:

• Idem. = I’m going.
• Znam. = I know.
• Vratit ću se. = I will return.

Odmah means immediately, right away, or straight away.

In this sentence:

• djeca mi odmah trče u zagrljaj
• = the children immediately run into my arms

Croatian word order is fairly flexible, so odmah can move, but not every position sounds equally natural.

This sentence is very natural as written because:

• mi is a clitic, and clitics tend to come early in the clause
• odmah then naturally follows

You may also hear:

• Djeca mi trče odmah u zagrljaj.
• Odmah mi djeca trče u zagrljaj.

But the original version is smooth and neutral.

Most naturally, it describes a habitual/repeated situation:

• Whenever I come home, the children immediately run into my arms.

That is probably the best way to understand it.

However, Croatian structures like Kad se vratim... can also be used for a future situation depending on context. The rest of the sentence would then usually make that clearer.

For example:

• Kad se vratim kući, djeca će mi odmah potrčati u zagrljaj.
• When I get home, the children will immediately run into my arms.

In your sentence, the plain present trče strongly suggests a general, repeated situation rather than a one-time future event.