I have never used a dating site and have not approached dating in the way you seem to do so my experiences may not be all that relevant. I did get overwhelmed by some of a partner's stuff and she has been seeing a therapist for over 20 years. Her parents were monsters. I sometimes do have to say I can't listen to her details and I am extremely glad she has a therapist to tell such things to.
In terms of getting to know someone - I take it slow and talk about things slowly. I don't divulge everything at once and I would be overwhelmed by someone who did it to me. I, for example, would have probably said I wanted to put off talking about my family until we met in person, or just stated they were challenging and gone on and talked a bit more at further conversations. But that is just how I do it.