Bad Idea Number One is to establish once and for all that Thérèse is a Very Bad Person who can't love anyone because she gets in the way of the Pattersons doing what they want to whom they want whenever they want. This would be done by having her spout dialog that is meant to show us that instead of actually caring a rat's ass about Françoise, she's only doing this to jerk Anthony and Liz around because she thinks she's better than they are.
Bad Idea Number Two is to establish that the legal system is a system of organized unfairness because it gets in the way of the Pattersons doing what they want to whom they want whenever they want. Proper legal procedure, the rules of evidence, the right other people have to plead their case without intimidation by clannish scum like the Foobs, all of it would be a very bad thing because it doesn't allow entitled vermin to screw people over unmolested.
The fun part is that Lynn's attempts to establish said Very Bad Ideas will backfire on her. For instance, her attempt to turn Thérèse into an evil, hypocritical monster who's only doing this to hurt Anthony and Liz because she's evil and insane and evil because she won't admit that Liz MUST go where she wants, the feelings and fears of other people be damned, will instead make her look like a sane, decent woman trying to protect her child from the crouching, jealous clan of ignoble hicks who treated her like a pariah.
Similarly, her attempt to show us that the court system is filled with people who have no sense of human will remind us that the law is established to protect decent people from having their rights arbitrarily violated by self-serving vermin like John and Elly. Despite the fact that swarming clusters of imbeciles would weep bitter, angry tears because real justice was done and hateful boors punished, the likes of us would be able to take comfort in two things. First off, we'd get to bear witness to yet another attempt to make Anthony look good that made him look even worse than he did before it. Second, we'd have to realize that a real custody hearing would probably be less humiliating to the Pattersons as Anthony's lawyers would probably tell him to play ball or Thérèse's lawyers would surely ram the bat up his arse.