Salut Patrick,

https://progress.lawlessfrench.com/questions/view/so-dont-cannot-be-used-in-any-of-the-phrases

I think the above may help you.

Bonne Journée

Jim

Patrick, 'à cause de' is a prepositional phrase, but not a prepositional verbal expression.  

"Dont" is not used with prepositional phrases. 

"Dont"  is used to introduce a relative clause containing the structure 'verb de...'; it comes before the verb, not after '  dont j'ai besoin ', ' dont je parle ' etc. (Annuler in the following clause is not a prepositional verb either) 

A couple of 'exceptions' with façon and manière are noted in the lesson - not sure if there are other exceptions but can't think of any off the top of my head. 

Other uses of 'dont' - whose, or including (quantity) - do not fit here either.

De qui/dont/duquel = of/about whom, of/about which - with prepositional verbs with "de" (French Relative Pronouns)

Just to complement the answer, here is the correct translation:

Ma sœur, à cause de qui / de laquelle j'ai dû annuler ma soirée, ne s'est même pas excusée. .. My sister, because of whom I had to cancel my evening, didn't even apologize. (I know this isn't usual English diction but it is grammatically correct and follows closely the French sentence.)

Thanks to @Chris, @Jim, @maarten and @Cécile, I understand now! 

Thanks to @Chris, @Jim, @maarten and @Cécile, I understand now!