Uxor dicit se per vicum sinistrum non ituram esse, sed per vicum dextrum.

Because se is the reflexive pronoun, and it refers back to the subject of the main verb, uxor.

So:

• Uxor dicit se... = The wife says that she...
• The she inside the reported statement is the same person as uxor

If Latin used eam, that would normally mean her as someone else, not the wife herself.

This is very common in indirect statement:

• Marcus dicit se venire = Marcus says that he is coming
• Marcus dicit eum venire = Marcus says that that other man is coming

After verbs of saying, thinking, knowing, hearing, and similar verbs, Latin often uses an indirect statement construction instead of a that-clause.

The standard pattern is:

• accusative subject + infinitive

So here:

• se = the subject of the reported statement, in the accusative
• ituram esse = the infinitive verb of the reported statement

That is why Latin says:

• Uxor dicit se... ituram esse

rather than using a separate finite verb like English does.

Because the action is future relative to dicit.

• ire is the present infinitive: to go
• ituram esse is the future infinitive: to be going to go, or more naturally in English, that she will go

So the sentence is not just saying what she is doing now. It is reporting what she says about a future action.

Compare:

• dicit se ire = she says that she is going / goes
• dicit se ituram esse = she says that she will go / is going to go

Because ituram agrees with se, which refers to uxor, a feminine singular noun.

The future infinitive is formed with:

• future active participle + esse

And the participle must agree with the subject in gender and number.

So:

• masculine singular: iturus esse
• feminine singular: ituram esse
• neuter singular: iturum esse

Since the wife is female, Latin uses ituram.

It is the future active infinitive of eo, ire.

Formation:

• supine stem: itum-
• future active participle: iturus, itura, iturum
• then add esse

So:

• ituram esse = to be about to go, or in indirect statement, that she will go

This is the regular way Latin makes a future infinitive for active verbs.

Because they follow the preposition per, and per takes the accusative.

So:

• per vicum = through the street / along the street
• per vicum sinistrum = through the left street
• per vicum dextrum = through the right street

The adjectives sinistrum and dextrum are also accusative singular masculine because they agree with vicum.

Here per means something like:

• through
• along
• by way of

So per vicum sinistrum means that the route goes by the left-hand street.

Depending on context, English might translate it more naturally as:

• through the left street
• along the left street
• by the left street

The important thing is that per expresses movement by way of something.

Because Latin often leaves out words that are easily understood from the previous part of the sentence.

So the full sense is:

• se per vicum sinistrum non ituram esse, sed per vicum dextrum ituram esse

But the second ituram esse is omitted because it is obvious.

This is called ellipsis, and it is very common in both Latin and English:

• English: She is not going left, but right
• Latin: ... non ituram esse, sed per vicum dextrum

It negates the reported action as expressed in the first half of the contrast.

The sense is:

• she says that she will go not by the left street, but by the right street

Because the sentence is contrasted with sed, the negative is understood against the first route, and the second route is the corrected alternative.

So the meaning is not she will not go at all. It is she will not go by that route.

Yes, but in a normal Latin way. Latin word order is much freer than English word order.

The sentence puts the route first:

• se per vicum sinistrum non ituram esse, sed per vicum dextrum

This helps highlight the contrast between:

• per vicum sinistrum
• per vicum dextrum

A more mechanically arranged version might look like:

• Uxor dicit se non ituram esse per vicum sinistrum, sed per vicum dextrum

But the given order is perfectly natural Latin and gives emphasis to the contrasted routes.

Yes. A direct-speech version would be something like:

• Per vicum sinistrum non ibo, sed per vicum dextrum

That means:

• I will not go by the left street, but by the right street

When this becomes indirect speech after dicit:

• ibo becomes ituram esse
• the subject I becomes se

So direct speech and indirect speech correspond like this:

• direct: non ibo
• indirect: se non ituram esse

Yes, here they are ordinary directional adjectives:

• sinister = left
• dexter = right

They agree with vicus just like English left street and right street, though in smoother English we might say:

• the street on the left
• the street on the right

A learner may also notice that sinister in English has a negative meaning, but in Latin it can simply mean left without any sinister tone in a sentence like this.