Avia nepoti persuadet ut apud se maneat.

Because persuadeō in Latin normally takes the person persuaded in the dative.

So:

• avia = the grandmother
• nepoti = to the grandson / grandchild
• persuadet = persuades

A very literal structure is:

• The grandmother persuades to the grandson...

That sounds odd in English, but it is normal in Latin.
So nepoti is dative because it depends on persuadet.

After verbs like persuadeō, Latin often uses ut + subjunctive to express what someone is being persuaded to do.

So:

• persuadet = persuades
• ut maneat = that he should stay / to stay

This is a very common Latin pattern:

• alicui persuadēre ut... = to persuade someone to...

English usually uses an infinitive: persuades him to stay.
Latin instead prefers ut with a finite verb.

Because it is inside an ut clause after persuadet, and that kind of clause takes the subjunctive.

So:

• manet would mean he stays as a plain statement
• maneat means that he stay / that he should stay

Here the clause is not just reporting a fact. It expresses the content of the persuasion, so Latin uses the subjunctive.

This is a matter of sequence of tenses.

The main verb is persuadet, which is present. After a primary tense like the present, Latin normally uses the present subjunctive for action happening at the same time as, or after, the main verb.

So:

• persuadet ... ut maneat = she is persuading him to stay

If the main verb were past, you would usually expect the imperfect subjunctive:

• persuasit ... ut maneret = she persuaded him to stay

Apud with the accusative often means at the house of, with, or in the company of a person.

So apud se here means:

• with her
• at her place
• in her home

In this sentence, it does not just mean physical closeness; it strongly suggests staying at the grandmother’s house.

Because se is the reflexive pronoun. It refers back to the subject of its own clause.

Here the main subject is avia, so:

• apud se = at her own place

If Latin used apud eam, that would normally mean at her place where her refers to some other female, not back to the subject in the normal reflexive way.

So se shows that the place belongs to the grandmother herself.

Se is accusative, because apud takes the accusative case.

So:

• apud + accusative
• apud se = with her / at her house

Even though se is reflexive, it still has to follow the case required by the preposition.

The understood subject is nepoti—that is, the grandson or grandchild.

In smoother English, the idea is:

• The grandmother persuades her grandson to stay at her place.

Latin does not repeat the subject inside the ut clause here, because it is clear from the context. The person being persuaded is the one who is expected to stay.

It comes from nepos, nepotis, which can have more than one meaning depending on context, including:

• grandson
• descendant
• sometimes nephew

In this sentence, because the subject is avia (grandmother), learners will usually understand nepoti as to her grandson or more generally to her grandchild.

In Classical Latin, with persuadeō, the normal construction is:

• persuadēre alicuī ut + subjunctive

So this sentence is following the standard pattern. English prefers to stay, but Latin prefers ut maneat.

That is why the sentence does not use something like persuadet nepoti manēre as its regular classical structure.

The word order is normal and natural, but Latin word order is flexible.

The sentence is:

• Avia = subject first
• nepoti = dative object
• persuadet = main verb
• ut apud se maneat = subordinate clause

A Latin writer could change the order for emphasis, but this version is straightforward and easy to follow. The most important thing is not position, but the grammatical endings:

• avia = nominative
• nepoti = dative
• se = accusative after apud
• maneat = subjunctive

Yes. The ut + subjunctive clause after persuadet is commonly treated as an indirect command or substantive clause of purpose/result after a verb of influencing.

In simpler learner terms:

• someone tries to influence another person
• Latin then uses ut + subjunctive

So ut apud se maneat gives the action that the grandmother is trying to get the grandson to do.