Earlier this week, my husband and I went to see a play at the Meiji-za in Tokyo.

Cf. https://en.wikipedia.org/wiki/Meiji-za

It’ was based on the Japanese famous comic “Sazae-san” by Machiko Hasegawa.

The TV anime series remains very popular, even after the death of its author, and the tits author passed away in 1992. Tickets for the stage adaptation was very difficult to obtain, but we managed to get two for the final performance.

The Meiji-za Theater is located in Ningyoōchoō, a downtown entertainment district that has flourished since the Edo era.

Through this play “Sazaesan, I would like the audienceMORE NATURALLY: I hope this play will encourage the viewers to reconsider what a family is.

It’s based on the famous Japanese famous comic “Sazae-san” by Machiko Hasegawa.

English adjective order is weird and I don't know a good pattern or source for it, sorry! But "famous" goes before nationality.

The (TV) anime series remains very popular even after the death of its author, and the tickets for the stage adaptation wasere very difficult to obtain, but we managed to get two for the final performance.

TV can be omitted here and would normally be.

Watch out for plurals: "The ticket was / the tickets were"

Sazae-san is a housewife who lives with her parents, siblings (her younger brother and sister) and, husband and son.

In these days, when nuclear families are norm(the norm / normal), this type of family structure is extremely rare, so it feels both nostalgic and strange.

(the) "norm" is a noun
"normal" is an adjective

To be honest, I feel a little envious when I compare it to my own family, where our parents have already passed away and our children live separately with little contact with us.

In fact, our family areis on the verge of falling apart as my husband and I are supposed to spend weekends apart.

"our family is" -> the subject is the family itself
"our family are" -> the subject is the individuals within the family

Sometimes the difference doesn't matter (e.g. our family are going to the beach / our family is going to the beach - both fine). But when you talk about the family structure itself falling apart, it's more natural to talk about the family itself as the topic.

Maybe, all the members of our family value individual freedom too much.

Through this play “Sazae-san", I would like the audience to reconsider what a family is.

It’s based on the famous Japanese famous comic “Sazae-san” by Machiko Hasegawa.

The TV anime series remains very popular even after the death of its author, and the tickets for the stage adaptation wasere very difficult to obtain, but we managed to get two for the final performance.

Sazae-san is a housewife who lives with her parents, siblings (younger brother and sister) and, husband, and son.

There are goodups and bad things going ondowns, but the family stays together, supports each other, and enjoys life.

"There are good and bad things going on" isn't wrong necessarily, but it doesn't sound like how I would expect most people to say this. "Ups and downs" is a very common way of referring to when a mix of good and bad things happen, especially in the context of relationships. You could also say "There are good times and bad times" which is another common way of expressing this.

In tThese days, when nuclear families are the norm, this type of family structure is extremely rare, so it feels both nostalgic and strange.

To be honest, I feel a little envious when I compare it to my own family, where our parents have already passed away and our children live separately with little contact with us.

In fact, our family areis on the verge of falling apart as my husband and I are supposed to spend weekends apart.

You could also say "our family is on the verge of collapse".

Maybe, all members of everyone in our family values individual freedom too much.

I think this is the most natural way of saying what you have written in the Japanese, but you could also say "Maybe our family values individual freedom too much." as well.

Through this play, “Sazaesan", I would like the audience to reconsider what it means to be a family is.

It’s based on the famous Japanese famous comic “Sazae-san” by Machiko Hasegawa.

It's more natural sounding to say "famous Japanese comic" rather than "Japanese famous comic". In English, there is a preferred order to adjectives, and usually adjectives that are an opinion or general opinion ("famous") come before adjectives that refer to the noun's origin ("Japanese"). You can read more about it here: https://www.rarejob.com/englishlab/column/20220320/#2

The TV anime series remains very popular even after the death of its author, and the tickets for the stage adaptation wasere very difficult to obtain, but we managed to get two for the final performance.

Sazae-san is a housewife who lives with her parents, siblings (younger brother and sister), and husband and son.

There are good and bad things going on, but the family stays together, supports each other, and enjoys life.

You could also say "There are ups and downs, but the family stays together"

In tThese days, when nuclear families are the norm, this type of family structure is extremely rare, so it feels both nostalgic and strange.

To be honest, I feel a little envious when I compare it to my own family, where our parents have already passed away and our children live separately with little contact with us.

In fact, our family areis on the verge of falling apart as my husband and I are supposed to spend weekends apart.

Maybe, all the members of our family value individual freedom too much.

Through this play “Sazaesan", I would like the audience to reconsider what a family is.

I think it may be more natural to say "reflect" as in "I would like the audience to reconsider what a family is". "Reconsider" has an objective feel, while "reflect" has the feeling of thinking about something deeply and/or philosophically.

The TV anime series remains very popular even after the death of its author, and the tickets for the stage adaptation wasere very difficult to obtain, but we managed to get two for the final performance.

In tThese days, when nuclear families are the norm, this type of family structure is extremely rare, so it feels both nostalgic and strange.

To be honest, I feel a little envious when I compare it to my own family, where our parents have already passed away and our children live separately with little contact with us.

In fact, our family areis on the verge of falling apart as my husband and I are supposed to spend weekends apart.

Maybe, all members of our family value individual freedom too much.

"All members of our family" is not wrong but is a bit unnatural. "Maybe everyone in our family values..." would sound better.
Since the sentence without "maybe" can exist by itself there shouldn't be a comma after "maybe", but I think this is very minor.

Through this play “Sazaesan, I would like the audience to reconsider what a family is.

If you're using "this" you don't need to name the play. Alternatively, you could say:
Through the play "Sazaesan"...
or just
Through "Sazaesan"...