Pater coniugi suae dicit viaticum inter liberos aeque dividendum esse.

It has two parts:

• Main clause: Pater coniugi suae dicit = The father says/tells to his wife
• Indirect statement: viaticum inter liberos aeque dividendum esse = that the travel money/provisions must be divided equally among the children

So the sentence is built around dicit, and everything after that reports what is being said.

Because coniugi suae is the person to whom the father speaks.

With dicere, Latin can use the dative for the person addressed:

• alicui dicere = to say/tell to someone

So:

• coniugi = to the spouse
• suae = his own

Together, coniugi suae means to his wife / to his own spouse.

Because suus, sua, suum normally refers back to the subject of its own clause.

Here the subject of the main clause is pater, so:

• coniugi suae = to his own wife, referring back to pater

If Latin used eius, that would usually point to someone else’s wife, not the father’s own wife.

So suae is the natural reflexive possessive here.

Yes. Coniunx can mean spouse, either husband or wife. The noun itself does not always show gender clearly in a given form.

Here the adjective suae is feminine singular, so it tells you that the spouse is female. That is why coniugi suae means to his wife rather than to his husband.

Syntactically, viaticum is the accusative subject of the indirect statement.

After verbs like dicit, Latin often uses accusative + infinitive to express reported speech. In that construction, the subject of the reported statement goes into the accusative.

So in:

• dicit viaticum ... dividendum esse

the thing being talked about is viaticum, and Latin treats it as the subject of the infinitive phrase.

A small detail: viaticum is a neuter second-declension noun, so its nominative and accusative singular look the same. The form does not change, but its function here is accusative.

Yes.

After a verb of saying such as dicit, Latin commonly uses indirect statement, also called the accusative-and-infinitive construction.

Here:

• viaticum = accusative subject
• dividendum esse = infinitive phrase

So literally the structure is something like:

• The father says the travel-fund to-be-divided...

But in natural English we say:

• The father says that the travel money must be divided...

Dividendum esse is a gerundive + esse construction, often called the passive periphrastic.

It expresses necessity, obligation, or something that has to be done.

So:

• dividendum esse = to have to be divided
• more naturally, must be divided

Because it agrees with viaticum, it is neuter singular:

• viaticum ... dividendum esse = that the viaticum must be divided

Because it agrees with viaticum.

The gerundive behaves like an adjective, so it must match the noun it belongs to in:

• gender
• number
• case

Since viaticum is:

• neuter
• singular
• syntactically accusative

the gerundive appears as dividendum, which is the matching neuter singular form.

The sentence does not explicitly state the agent.

The passive periphrastic often tells you that something must be done, without saying who must do it. So here the focus is on the necessity:

• the viaticum must be divided equally among the children

If Latin wanted to name the responsible person, it could add a dative of agent. But in this sentence, the agent is simply left unstated.

English often does the same thing:

• It must be divided
  without saying by whom.

Because inter takes the accusative case.

So:

• inter liberos = among the children

This is completely normal Latin usage.

Also, liberi in the plural often means children in a family context, not just free people. So here liberos means the children.

Aeque is an adverb, so it modifies the verbal idea dividendum esse.

It tells you how the dividing is to be done:

• aeque dividendum esse = must be divided equally

So aeque does not describe liberos or viaticum as adjectives would; it describes the action of dividing.

Because Latin relies much more on case endings than on word order to show grammatical relationships.

English usually needs a fairly fixed order:

• subject + verb + object

Latin is much freer because forms like coniugi, liberos, and dividendum already show their roles.

This sentence is arranged quite naturally for Latin:

• Pater = subject first
• coniugi suae = person addressed
• dicit = main verb
• then the reported statement

The order also helps group related ideas together, especially the infinitive clause at the end. Even if some of the words were rearranged, the basic meaning would stay the same.

Because Latin normally does not use a separate word equivalent to English that when introducing indirect statement after verbs like say, think, know, and so on.

Instead, Latin switches to the accusative-and-infinitive construction.

So English says:

• The father says that the money must be divided

But Latin says, more literally:

• The father says the money to have to be divided

That sounds strange in English, but it is standard Latin grammar.