Millicent is an elitist without the benefit of an elite society. Truth is, the other residents can't stand her, because she's a quarrelsome busybody; therefore, she never gets invited to any of the tower's intimate social events. She spends her days hanging around the house or complaining to her poor husband.
If you take the love letter off Susan Lancaster's desk and take it to Millicent, she will immediately run off to find her husband; she will proceed to kill him with her 10mm pistol, and go after Susan herself (the guards seem not to mind). After both murders are committed, she will abandon Tenpenny Tower for the wasteland. You may find her wandering around Warrington Trainyard afterwards. If you attempt to speak to her, she will only say that she loved Edgar and feels "lost" without him.
If the player decides to deal with the "Tenpenny Tower" quest by killing Roy Phillips and his gang before giving Millicent the Love Letter, then you will not be able to give it to her as you will not go in to dialog with her, she will only tell you well done for dealing with the ghouls.
She cannot be shown the love letter if the player first successfully passes the speech check meant to force her out of the tower.
If you attempt to steal from her and are caught the moment before she begins firing on her husband, she'll put away her pistol to take back whatever you stole. She will then just stand in place without attacking, and Edgar will act like nothing ever happened. She will no longer initiate conversation with the player ("I can't talk now" is all she will say) and will never move from the location where she was pickpocketed unless attacked or killed. [platforms tag needed]
If you kill her before without any contact or quest related activation, you may not find the pistol that she kills her husband with. [platforms tag needed]
If you kill her just before she shoots one of her victims, that person will die, despite not being shot. This is because it's a scripted scene, which is also why she is never attacked by the security in the tower for the murder of her husband and Susan Lancaster. [platforms tag needed]
After giving her the love letter, she will confront her husband about the matter. If you wait until she is done speaking to her husband, you can pickpocket 10mm rounds (10) from her. She will then empty the magazine on her husband and when she is done she will run to Susan Lancaster and proceed to shoot her although she doesn't have any ammunition. [platforms tag needed]
Sometimes after you show her the love letter she will kill her husband and Susan then walk to the entrance and get stuck in the corner near the tables. [platforms tag needed]
If you convince her, but fail at convincing her husband before trying to give her the love letter, she won't have any dialog option. So, the only way to complete the quest in that case is to kill the husband or to raid the hotel with the feral ghouls. [platforms tag needed]
If you reverse-pickpocketing a better weapon (and correspondent ammunition) she will not be able to kill her husband as she will try to use her pistol instead without firing it. She will make some funny movements as she will take out and holster her pistol indefinitely. [platforms tag needed]
If you already enslaved Susan Lancaster and confirmed she is in the slave pen, Millicent will somehow kill her in the slave pen at Paradise Falls after seeing love letter. [platforms tag needed]
If you give her the love letter while she is sitting at the table with her husband, she will get up but won't kill him. [platforms tag needed]