The story has an unreliable narrator, baby doll is a character that can't be trusted, she is either insane or is mentally escaping in a fantasy world due to all the trauma she is encountering.

The first escape is in a brothel, she is lying to herself to give her some form of structure, she is lying to herself to allow her to cope. While a brothel may not seem like a place you want to escape to it does share some similarities with reality while getting rid of the worse ones. The closeness to reality makes it easier for the mind to grapple with the situation.

In the brothel she is merely an orphan sent to a brothel compare this to reality
1) Her mother recently died in reality
2) Her sister is murdered via her step father, and she was framed for the murder
3) She has a serious confrontation with her step father where she almost kills him with the gun, before breaking down in her tears
4) She isn't committed via her stepfather and "sentenced" to get a lobotomy (her stepfather does this as well as the murder of his other stepdaughter to claim the inheritance his wife left nothing for himself but instead her daughters.)

Remember also in the brothel she is merely dancing to her "clients"/"distracting the guards". Dancing is sorta empowering for you have the control of the situation, you control the titulation, while in reality
5) Baby Doll is being raped via the orderlies

Now Baby Doll has a fantasy inside a fantasy. In her second fantasy she and the other mental patients are super powered heroines, in this fantasy she is in control. Her mind does this for two reasons to re-establish security and to give herself the courage to try to escape. In her second fantasy she is not purposefully try to get raped (which she is doing in reality), to distract the orderlies so her fellow heroines can achieve their goals, no she is a super-heroine on a mission, a dangerous mission but a mission with a clear goal in mind.

Baby Doll is an unreliable narrator, and thus we can't tell what really happened with Amber, Blondie, and the Dr/Madam Vera Gorski. We can't tell if in the brothel what words the Madam gave (you are safe, don't be afraid, you have all the weapons you need) occurred right before the first rape/first action theory at all or if they really occurred at all and instead baby doll imagined the Madam Vera Gorski saying them since she trusted the psych.

That said I am not surprised via the possibility that Babydoll wanted to escape but when that failed she really wanted the lobotomy, she had a series of traumatic experiences the last two weeks of her life and she wanted to be free even if that means a lobotomy and mental suicide.