In English: We use subject pronouns, really? Didn't know that.

Yes, you are correct. That's as close as you can come to a stress pronoun in English.

My brother and me -- Mon frère et moi.
My brother and I (sounds a bit stilted) -- Mon frère and je (plain wrong).

-- Chris (not a native speaker).

Eh... I only rarely hear constructions like "Doug and me played cards." Not even informally, among friends, or when messaging. It would be considered an error to us. Maybe it's regional.

But "John and I were friends" is never wrong and doesn't sound the least bit stilted to me!

“Hugo and they” is grammatically correct English (technically) but you and pretty much everyone else would say “Hugo and them”   

Well, many English speakers will get this wrong. Often, we hear it said incorrectly so much, that correct grammar sounds incorrect.  But it should be "My daughter and they play together." If you leave off "My daughter" would it be correct to say, "Them play together?" No. "They play together." When it's a compound subject, you are supposed to use subject pronouns. 

Angie, the subject is the whole "My daughter and them". Taking only a piece of a subject doesn't need to make sense.

It would be like saying "My landlord is mean" is wrong because "Landlord is mean" doesn't make sense...

Did you never have to diagram a sentence?  Subject pronouns have to be used for the subject. 

" diagram a sentence? " Huh? What kind of English is that? Did you never hear anyone say a sentence in English? Because " My daughter and they play together " sounds like the stupidest of Shakespearean outdated English.

Angie is correct!  Along the same lines, it is incorrect to say that "He and me went to the store":  Broken down to two sentences, it would be "He went to the store" and "I went to the store".  So when the subject is compound, the correct version is "He and I went to the store".

Personally I would say "My daughter plays together with them."