And lest the post end on a bland note here's my theory on why Becca never called Frank "Dad" when they were family, even if Lilli wasn't a factor:
The dynamic was very Shannon-heavy with the following dynamics from Shannon's point of view:
Shannon despised Abby, tolerated Frank, Becca, and maybe Lilli.
Frank loved Shannon, saw Becca, Abby and Lilli as his daughters
Becca was neutral towards Frank but positive towards Abby and occasionally nasty towards Lilli, had respect for her (Shannon)?
Lilli respects (possibly fears somewhat?) Shannon, despises what Frank stands for, adores Abby and has a difficult relationship with Becca
Abby fears Shannon, loves Frank as her father, Lilli and Becca are like sisters to her (or Lilli a little more so).
Which thus brings us to the following scenario:
Abby was Team Frank, Lilli was Team Shannon, albeit more out of "fear" and because she didn't like Frank. Becca was pretty much neutral. This means that the teams were very evenly matched. Now if Becca had openly shown sympathy apart from the due respect, then the balance would have shifted in favor of Frank, possibly Becca and Abby would have even pulled Lilli into Team Frank's boat, so Team Shannon would have been just Shannon. At least, I can imagine Becca thinking something like that, which her mother might think. And I think that this assumption is even realistic: Shannon has already shown for me in the flashbacks in the first meeting with Frank that she has at least narcissistic personality traits and I also think it is absolutely likely that aside from the initial attraction towards Frank, before she knew that he and Jessica were friends, she only dated him later out of resentment towards Jess to hurt her.
The scene with the judge, the fact that she never did anything to help Lilli get over the pain of losing her father (though I would even argue in her favor here that psychotherapy is still stigmatized and hard to get) and her behavior towards Abby (just because she looks like Jessica) clearly show to me that Shannon is only interested in one person, and that is herself. To others, she only does things that benefit herself in the long run:
Shannon is dating Frank? Just to get one over on Jess. The fact that Frank was well endowed was a bonus.
Shannon later marries Frank and tries to be a mother to Abby? She just won't have felt like having to deal with Lilli's problems anymore (which we saw in flashbacks was actually done to a large extent by Frank). She will have only put up with Abby so that Frank would stay.