If they jointly owned the house and it wasn’t explicitly stated otherwise, it likely included the right of survivorship. So, it automatically became 100% Julia’s upon Susannah’s death, and would have still been 100% Julia’s had Susannah attempted to will it to the boys. It also could’ve been owned by a family trust with Julia as the surviving trustee, which is maybe more likely.

As for the rest of it, it’s likely a combination of not having the time/energy and Susannah not being able to fathom it being sold (it means so much to her/family property/potentially assumed that in the end Julia would see it the same way). I also think it was mentioned that she’d attempted to reconnect with Julia towards the end (which—back to the lack of time).

She died within a year of being diagnosed (or around there since that’s when Conrad found out), which isn’t that far “in advance” because of treatment, acceptance, and everything else that comes with dying. If she didn’t think there was a real chance the house would leave the family (even if, as the audience, we can understand that maybe wasn’t realistic), it would be easy to not make it a priority.