Maybe I'm misreading the situation, but I'm not seeing a whole load of communication going on here.
You ask us not to judge that you're telling your boyfriend to willingly conceal information from his other girlfriend, but then you get mad at her because she's taking a certain night... it just sounds like noone's talking to each other here, or that you're all going through the boyfriend and he's not managing to get the right messages accross.
Have you met this girl? Are you all actively communicating to each other? Does she know that you want Saturdays or are you just hoping your boyfriend will sort it all out.
One of my personal "rules" in poly is that if I want communication expressed, then I express it myself. If you rely on other people to communicate for you, then messages get mixed and your interests aren't taken care of.
Also, what's so good about Saturday that isn't good about Friday?