Con ese uniforme, no pude reconocer a mi hija en el patio.

Starting with Con ese uniforme puts the emphasis on the uniform as the reason for the problem.

• Con ese uniforme = With that uniform / Wearing that uniform
• It gives the context first: because of that uniform, I couldn’t recognise her

You could also say:

• No pude reconocer a mi hija en el patio con ese uniforme.

That is also grammatical, but it sounds a little less focused on the uniform.

Because uniforme is a masculine noun in Spanish.

Even though it ends in -e, nouns in Spanish are not always feminine unless they end in -a. So:

• el uniforme
• ese uniforme

If it were feminine, it would be:

• la chaqueta
• esa chaqueta

So here ese agrees with uniforme in gender and number.

Ese means that and points to something not especially close to the speaker.

Spanish has three main demonstratives:

• este / esta = this
• ese / esa = that
• aquel / aquella = that over there

So ese uniforme means that uniform.

In real speech, the difference between este and ese can sometimes be a bit flexible, but the basic idea is:

• este = nearer
• ese = a bit farther away / already known in the conversation

Pude is the preterite of poder, and it refers to a completed event in the past.

• no pude reconocer... = I couldn’t recognise... on that specific occasion

This sentence is about one finished moment: the speaker tried to recognise their daughter in the playground and failed.

If you said no podía, that would usually suggest:

• an ongoing inability
• a repeated situation
• background description

For example:

• Con ese uniforme, no podía reconocerla desde lejos.
  = With that uniform, I wasn’t able to recognise her from far away.

But in your sentence, no pude fits the idea of one completed event.

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

The verb form pude already tells you the subject is I:

• pude = I could / I was able to

So (yo) no pude reconocer... is possible, but yo is usually omitted unless you want emphasis or contrast.

For example:

• Yo no pude reconocer a mi hija, pero mi marido sí.
  = I couldn’t recognise my daughter, but my husband could.

Because reconocer means to recognise, while conocer means to know / to be acquainted with.

• conocer a alguien = to know someone
• reconocer a alguien = to recognise someone

So:

• No pude reconocer a mi hija = I couldn’t recognise my daughter
• No conozco a tu hija = I don’t know your daughter

This is a very common distinction for English speakers to learn.

That is the personal a.

In Spanish, when the direct object is a specific person (or sometimes a pet), you usually put a before it.

So:

• reconocer a mi hija
• ver a María
• llamar a mi padre

But:

• ver el coche
• reconocer la casa

The a does not mean to here. It is just a grammar marker used before a personal direct object.

Yes. Once it is clear who you mean, you can replace a mi hija with the direct object pronoun la:

• Con ese uniforme, no pude reconocerla en el patio.

That means the same thing: I couldn’t recognise her in the playground.

Use a mi hija when you want to name the person clearly. Use la when the reference is already understood.

In Spain, patio often means a courtyard, playground, or schoolyard, depending on context.

In this sentence, en el patio most naturally suggests something like:

• the school playground
• the courtyard area
• the place outside where children are gathered

So it may not mean patio in the English house/garden sense only. In Spain, it is a very common word for a school outdoor area.

In Spanish, no normally goes directly before the conjugated verb.

So:

• No pude reconocer... = correct

This is the standard way to negate the verb phrase.

Compare:

• Pude reconocer a mi hija. = I was able to recognise my daughter.
• No pude reconocer a mi hija. = I was not able to recognise my daughter.

No, Spanish word order is fairly flexible, but changes in order usually change emphasis, not basic meaning.

Original:

• Con ese uniforme, no pude reconocer a mi hija en el patio.

Possible alternatives:

• No pude reconocer a mi hija en el patio con ese uniforme.
• En el patio, no pude reconocer a mi hija con ese uniforme.

All of these can work, but they highlight different parts of the sentence:

• Con ese uniforme... focuses first on the uniform
• En el patio... focuses first on the location
• beginning with No pude... sounds more neutral

So the original sentence is natural because it foregrounds the reason: that uniform.

In normal context, it means the daughter was wearing that uniform.

Spanish often leaves this kind of thing implicit when it is obvious from the meaning. Since the problem is recognising my daughter, the natural interpretation is:

• With that uniform on, I couldn’t recognise my daughter...

In theory, without context, con ese uniforme could be attached differently, but real speakers will almost always understand it as referring to the daughter’s appearance.