Whenever her parents have guests, Beth always wants to join in the adults' conversation.

Literal

Parents [to-に] guests [subject-が] exist time [topic-は], always Beth [topic-は] adults [possessive-の] conversation [to-に] want-to-enter.

~たがる (to show signs of wanting to) is the third-person desire form of ~たい — used because the speaker is describing Beth's wants, not their own. いつも (always) sets the habitual pattern. お客さん uses the honorific お~ prefix casually.