I think her obsession with owning a (big, apparently) house comes from a mixture of entitlement and jealousy. She’s deeply jealous of Jamie for example, and I think that’s why she started the pile-on back in March. She thinks he has the career (and money and success) that she should have had. She is too self-obsessed and deluded to appreciate that his success was largely due to talents which Jack simply doesn’t have (as evidenced by her turns on DKL and Hellmann’s).
She also lived with a multi-millionaire for a while, and would have assumed she was set for life and would always live in a big swanky (not rented) house (courtesy of Allegra’s hard work). But she fucked that up. Then she was with Louisa - also very comfortably off, house ownership wouldn’t have been a problem, all paid for by Louisa’s hard work. And she fucked that up.
Now her only option is to pay for it herself, through her own work, and she really doesn’t see why she should. So she stamps her foot and screams like a toddler.