That's one way to stop them having anyone stay over...
I can translate it as «Мои дочери не имеют кроватей» (и это будет понятной конструкцией для русского). But this variant isn't corrent.
I'm native and understand it, but it sounds very unusual
This is what I wrote as well. It definitely should be accepted. "У моих" (or whatever pronoun) is not the only way to express possession in Russian.
That нит is doing a lot of work in this sentence.
Is there another way to say do not have ?