Después de haberse roto el cordón de mis zapatillas, tuve que volver a casa.

Both are possible, but they are built differently.

• después de + infinitive = after + -ing / after having ...
• después de que + finite verb = after ... happened

So:

• Después de haberse roto el cordón... = After the lace had broken / after the lace broke...
• Después de que se rompió el cordón... = After the lace broke...

The version with después de + infinitive is very common when the subject is understood from context or when Spanish prefers a more compact structure.

It is a perfect infinitive of the pronominal verb romperse.

Breakdown:

• haber = auxiliary verb
• se = reflexive/pronominal marker
• roto = past participle of romper

So haberse roto literally means to have broken / to have become broken.

It expresses an action that happened before the action in the main clause:

• first: the lace broke
• then: I had to go home

That is why the perfect infinitive is used.

Because with an infinitive, Spanish normally attaches pronouns to the end of the infinitive.

So:

• romperse = to break / to get broken
• haberse roto = to have broken / to have gotten broken

You cannot say:

• después de se haber roto ❌

The pronoun must stay attached:

• después de haberse roto ✅

This is the normal position of pronouns with infinitives, gerunds, and affirmative commands.

Because the sentence means that the lace broke, not that someone broke the lace.

Compare:

• romper algo = to break something
  
  • Rompí el cordón. = I broke the lace.
• romperse = to break / to get broken
  
  • El cordón se rompió. = The lace broke.

In this sentence, the lace is presented as the thing that ended up broken, not as a direct object deliberately broken by someone.

Not in the literal English sense of it broke itself.

In many grammar explanations, romperse is called a pronominal or pseudo-reflexive verb here. The se often marks that something undergoes a change of state:

• La puerta abrió. is not normal in Spanish
• La puerta se abrió. = The door opened

Likewise:

• El cordón se rompió. = The lace broke

So it is best to learn romperse here as the normal way to say that something broke.

Because tuve que presents the obligation as a completed, specific event in the past.

• tuve que volver = I had to go back
  A concrete thing that happened.
• tenía que volver = I had to / was supposed to go back
  More descriptive, habitual, ongoing, or backgrounded.

In this sentence, the speaker is telling a sequence of events:

1. the lace broke
2. I had to go home

That favors the preterite: tuve que.

In Spanish, casa often appears without an article when it means home in a general personal sense.

• volver a casa = to go back home
• estar en casa = to be at home
• llegar a casa = to get home

If you say la casa, it sounds more like the house/building rather than home.

So:

• volver a casa = natural here
• volver a la casa = possible only in more specific contexts, like a particular house

This is just a natural way to be specific.

• el cordón = the lace
• de mis zapatillas = of my trainers/sneakers

So the phrase identifies exactly which lace: the one from the speaker’s shoes.

A few notes:

• zapatillas in Spain usually means trainers / sneakers
• zapatos is more general and often sounds more like shoes
• mi cordón would sound odd unless context already made it very clear what kind of cord it was

Because zapatillas refers to the pair of trainers/sneakers or to the shoes as a set.

Spanish often uses the plural naturally for things that come in pairs:

• mis gafas = my glasses
• mis pantalones = my trousers/pants
• mis zapatillas = my trainers/sneakers

So el cordón de mis zapatillas means the lace of my trainers, even if only one particular lace broke.

Yes, and it is very similar, but there is a slight difference in emphasis.

• Después de romperse el cordón...
• Después de haberse roto el cordón...

Both can mean after the lace broke.

The version with haberse roto makes the prior completion a bit more explicit, like after having broken. In many everyday situations, both are acceptable, but the perfect infinitive often sounds a little more formal or more precise about the sequence.

Yes, and in everyday Spanish that can sound very natural.

• Se me rompió el cordón literally looks like the lace broke on me
• It often expresses that something happened to you, often unintentionally or inconveniently

So:

• Después de que se me rompió el cordón de las zapatillas, tuve que volver a casa.

This version adds the idea that the breakage affected the speaker personally. It is a very common Spanish way of expressing these situations.

Because it is used with haber, and past participles used with haber do not agree in gender or number.

So:

• ha roto
• habían roto
• haberse roto

always use roto, not rota/rotos/rotas.

Compare that with adjectives:

• el cordón está roto = masculine singular
• las zapatillas están rotas = feminine plural

So in your sentence, roto is part of the verbal form, not an adjective.

Here después de functions as a fixed expression meaning after.

Common patterns:

• después de + noun
  • después de la clase = after class
• después de + infinitive
  • después de comer = after eating
  • después de haberse roto... = after having broken...

So it is best to learn después de as a unit.

Yes, to some extent.

Original:

• Después de haberse roto el cordón de mis zapatillas, tuve que volver a casa.

Other natural possibilities:

• Tuve que volver a casa después de haberse roto el cordón de mis zapatillas.
• Después de que se rompió el cordón de mis zapatillas, tuve que volver a casa.

Spanish often allows more flexibility than English, but the original order is very natural because it sets up the cause/background first and then gives the result.

It is grammatical and understandable, but in everyday speech many people might choose a simpler version, for example:

• Se me rompió el cordón de las zapatillas y tuve que volver a casa.
• Después de que se me rompiera el cordón de las zapatillas, tuve que volver a casa.
• Al romperse el cordón de mis zapatillas, tuve que volver a casa.

Your original sentence is perfectly fine, but it sounds a little more written or carefully structured than the most casual spoken option.

In Spain, zapatillas often means trainers / sneakers.

This matters because vocabulary can vary across the Spanish-speaking world:

• In Spain: zapatillas commonly refers to sports shoes or casual trainers
• In some other countries, zapatillas may mean something slightly different depending on the region

So for Spanish from Spain, mis zapatillas is a very normal choice for my trainers/my sneakers.

Cordón is a general word meaning cord, string, lace, or drawstring, depending on context.

In this sentence, because it is linked to zapatillas, it clearly means shoelace.

So:

• el cordón de mis zapatillas = my shoelace / the lace of my trainers

Context tells you which English translation is best.