Learn Hardcore Japanese: tuma ha otto ni, bangohan no ato de sara wo arau you ni tanomimasita. - The wife asked her husband to wash the dishes after dinner.

は marks the topic: what the sentence is "about." In this sentence, 妻 (the wife) is also the doer of the main action 頼みました ("asked"), so topic and subject happen to be the same. Using 妻は presents "the wife" as known information and then tells us what she did. You could also say 妻が夫に…頼みました, which puts more emphasis on who did it ("it was the wife who asked…") rather than just setting her as the topic.

Why is 夫 followed by に instead of を?

夫に marks the husband as the person the action is directed to. With 頼む, the core patterns are:

人に頼む – to ask someone (for a favor / to do something)
ものを頼む – to request / order something (e.g., food, a service)

Here, the wife is asking the husband to do something, so the husband is the indirect object and takes に: 夫に … 頼みました.
If you said 夫を頼みました, it would instead mean something like "relied on the husband" or "asked for the husband (as the requested thing)," which is different.

How does 晩ご飯のあとで work grammatically?

Breakdown:

晩ご飯 – dinner
の – "of," linking two nouns
あと – "after / later," literally "the time after"
で – particle making the whole phrase function as a time adverbial

So 晩ご飯のあと is "the time after dinner," and 晩ご飯のあとで means "after dinner (at that time), …". This follows a common pattern:

N のあとで V – do V after N
e.g. 授業のあとで帰ります。 – "I go home after class."

You can usually also say 晩ご飯のあと皿を洗う (dropping で) with almost no change in meaning, but ～のあとで V is a very standard and natural pattern.

Could I use 晩ご飯のあとに instead of 晩ご飯のあとで? What's the difference between に and で here?

Both ～のあとに and ～のあとで are grammatically possible with あと.

～のあとに V often treats "after N" as a simple point in time: "at the time after N, V happens."
～のあとで V tends to emphasize "once N is finished, in that resulting situation, V happens."

In practice, with everyday actions like "wash," "go," "do," ～のあとで is more common and usually sounds more natural. So 晩ご飯のあとで皿を洗う is the typical choice; 晩ご飯のあとに皿を洗う is not wrong, just less usual.

Does 皿 mean one plate, or "the dishes" in general?

Literally, 皿 is "plate" or "dish" (singular). Japanese normally doesn’t mark plural explicitly, so 皿を洗う can mean "wash a plate," "wash the plates," or "wash the dishes," depending on context. Because it’s right after 晩ご飯 ("dinner"), the natural interpretation is "wash the dishes (from dinner)," so we translate it that way in English. If you want to clearly show plural, you can say お皿を全部洗う ("wash all the plates") or たくさんの皿を洗う ("wash many plates").

Why is 洗う in dictionary form? Why not 洗って or 洗います?

In the pattern [verb-dictionary-form] + ように + 頼む, the dictionary form is used because it represents the action you are asking someone to do. Tense and politeness are carried by 頼みました, not by 洗う. So:

皿を洗うように頼みました。 – "asked (him) to wash the dishes."

Forms like 皿を洗ってように頼みました or 皿を洗いますように頼みました are ungrammatical in this structure. Think of 皿を洗うように as "that he wash the dishes / to wash the dishes," functioning as the content of the request.

What does ように add here? Could I just say 皿を洗う頼みました?

You cannot say 皿を洗う頼みました; there must be something to connect the "content" clause to 頼みました. One very common pattern is:

V-dictionary-form + ように + 言う / 頼む / 注意する …

Here, よう is originally a noun meaning "way / manner," and に makes it adverbial: "in such a way that…". With verbs of saying and requesting, this combination has come to mean "tell/ask (someone) to V." So:

皿を洗うように頼みました。
≈ "asked (him) to wash the dishes."

In casual conversation, people may also say things like 皿を洗ってって頼んだ or 皿を洗ってと頼んだ, but in neutral/polite style Vように頼む is the standard form.

Is the に in ように the same particle as the に in 夫に?

Yes, it is the same particle に, but it attaches to different things:

In 夫に, に marks the indirect object ("to the husband").
In ように, に attaches to よう (a noun meaning "way / manner") and turns it into something adverbial: "in such a way that / so that."

So 皿を洗うように頼む can be seen as:

[皿を洗うように] – "in such a way that he washes the dishes"
頼む – "ask"

Together: "ask (him) so that he will wash the dishes" → "ask him to wash the dishes."

In 皿を洗うように頼みました, what is the direct object of 頼みました?

The direct object is the entire clause 皿を洗うように. Japanese often uses a [clause + ように] (or [clause + ことを]) as the "thing" that is said, thought, or requested. Structurally, you can analyze the sentence as:

妻は – as for the wife (topic)
夫に – to the husband (indirect object)
晩ご飯のあとで皿を洗うように – "to wash the dishes after dinner" (content of the request)
頼みました – asked (politely, past)

That mirrors English "She asked [him to wash the dishes after dinner]," where the bracketed clause is also the object of "asked."

What form is 頼みました, and how would this sentence look in casual speech?

頼みました is the polite past form of 頼む ("to ask / to request"):

Dictionary: 頼む
Polite non-past: 頼みます
Polite past: 頼みました

A natural casual version of the sentence would be:

妻は夫に、晩ご飯のあとで皿を洗うように頼んだ。

Here 頼んだ is the plain past form. The rest of the sentence stays the same.

Could I say 妻が夫に…頼みました instead of 妻は夫に…頼みました? What's the nuance?

Both 妻は夫に…頼みました and 妻が夫に…頼みました are grammatically correct.

妻は introduces "the wife" as the topic, usually something already known in the conversation. It sounds neutral and narrative here.
妻が emphasizes "the wife" as the doer, often when you’re identifying or contrasting the subject, e.g.:
夫が頼んだんじゃなくて、妻が夫に頼みました。 – "It wasn’t the husband who asked; the wife asked the husband."

Without that kind of contrast, 妻は… is the more naturally neutral choice.

Are there other common ways to say "asked her husband to wash the dishes" in Japanese?

Yes. Some common alternatives:

妻は夫に、晩ご飯のあとで皿を洗ってくれるように頼みました。
Adds くれる, emphasizing "do it for me / for us," making the favor aspect clearer.
妻は夫に、晩ご飯のあとで皿を洗ってくださいと頼みました。
Uses ～てくださいと頼む: she literally asked him, "Please wash the dishes after dinner."
妻は夫に、晩ご飯のあとで皿を洗ってほしいと頼みました。
Uses ～てほしい, expressing her desire: "asked him (saying) that she wants him to wash the dishes after dinner."

The original 皿を洗うように頼みました is a very standard, neutral "asked him to wash the dishes."

What is the difference between using ように and ために in sentences like this?

In this "ask/tell someone to do" pattern, you must use V-dictionary + ように + 言う／頼む, not ために. More generally:

V-辞書形 + ために – expresses a purpose that the subject intends and controls.
Example: 日本で働くために日本語を勉強しています。 – "I study Japanese in order to work in Japan."
V-辞書形 + ように – often expresses doing something so that a certain result will (hopefully) happen, and it’s also used with verbs of saying/requesting.

So 皿を洗うように頼みました means "asked (him) to wash the dishes."
皿を洗うために頼みました would be interpreted as "asked (someone) for the purpose of washing the dishes," focusing on the purpose of the asking itself, which is not what you want here.

Are the spaces between the Japanese words and the comma after 夫に normal in real Japanese writing?

Normally, Japanese text:

Does not have spaces between words.
Does use commas (、) to divide phrases, but their exact placement is somewhat flexible.

So in regular writing the sentence would typically appear as:

妻は夫に晩ご飯のあとで皿を洗うように頼みました。
or
妻は夫に、晩ご飯のあとで皿を洗うように頼みました。

The spaces you see are just a teaching aid to show word boundaries more clearly to learners.

Is there any difference between 晩ご飯 and 夕食?

Both can mean "dinner," but the tone is a bit different:

晩ご飯 – casual, conversational; literally "evening meal." Very common in everyday family contexts.
夕食 – slightly more formal or written; common in menus, hotel plans, schedules, etc.

In a family/household sentence like this, 晩ご飯 sounds very natural. You could say 夕食のあとで皿を洗うように頼みました, which is fine but feels a bit more formal or neutral.