The lesson seems to indicate that this separation is 'allowed' but 'irregular'.
However it seems frequent and intrinsic enough in some translations to deserve identifying and defining as a rule of syntax.
If the 'possession' is the 'object' of the verb in the following clause then it is separated from dont and put after the verb in that clause. 'Dont' here is like a relative pronoun joining two clauses. All the examples support this observation.
Tu as jeté la chaussure dont le talon est cassé.You threw away the shoe with the broken heel [lit. whose heel is broken]
BUT???Tu as jeté la chaussure chère dont j'ai cassé le talon.
Les enfants, dont je connais la maman, sont bien élevés.François, dont j'ai rencontré la femme le mois dernier
I think the most literal translation of dont is actually "of whom" or "of which", and it always follows the owner. Viewed this way, the usage is completely regular in all the examples you give.
I am sorry but while I am normally very appreciative of the knowledge and care and respect shown in ALL your replies, I think this post, seemingly made in haste, is dismissive of my observation. My observation may be WRONG and I included question marks and wording to allow for that and to seek insight as to the pattern contained in the examples within the lesson.
Une fille dont le frère ..better translated as 'whose brother'
Les enfants, dont je connais… better translated as 'whose mum'
J'ai rencontré cet acteur dont le nom... better translated as 'whose name.'
Of course one can reword the translation to say 'the name of whom'; 'the mum of whom; etc etc....
But doing so, especially for inexpert french learners like myself, will devalue ONE VERY significant grammar syntax ..The 'english wording 'whose mum' translates to french as 'don't la maman' … I patted myself on the back for having noticed that and tucked it away in hopes of recalling that 'oddity' in the future.... so i dont write 'dont maman'.
It is with that 'enjoyment' of the twist of the language that I posted my other observation in hopes that more qualified contributors, as yourself , will indulge me a questioning but not indifferent perusal.
I am sorry but to say that 'dont' simply translates to a literal conversion 'of whom' or 'of which' diminishes the lesson and the joy of it's nuance. Not to mention throwing into the garbage bin, my curiosity re the pattern of 'don't ' separated from the possession noun' when that possession noun is the OBJECT of the verb in the dependent clause.
I am sorry if my reply seemed dismissive, it wasn't meant to be. Actually, after I had posted it I did start to think that it was perhaps less useful than I had intended.
Of course, you're right that it's important to understand that "dont" needs to be translated as "whose" in some cases to give a natural translation.
I just thought that there was a simpler way of understanding the word order. If you think of "dont" as meaning "whose" then you expect it to be immediately followed by a possession, and then you need some rule to explain the cases when it isn't. But there are many things that can follow dont - a possession, a phrase concerning a possession, or any phrase with a verb followed by "de". I find it easier to think of it, initially, as "of whom/which" and then figure out the most appropriate translation later. But perhaps that's just me.
You might be interested in my answer to a query regarding the syntax with 'dont' in the examples given in this lesson -
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