You are Beth's father. You should continue to act like her loving father... You are not necessarily wrong to be upset about your daughter's use of social media to announce her newfound biological family members, but this sort of public sharing of what might seem like personal or private business has become almost the norm for people in her generation.
Beth pursued DNA testing after her mother's death in part to reveal any genetic health issues she might have inherited. She then quite naturally sought out other biological relatives in order to answer some of those questions she had never felt able to ask you.
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