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 the Lone Wanderer takes the love letter off Susan Lancaster's desk and takes 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 and head for the Warrington trainyard, where she will head into the tunnels, supposedly to meet her death by the hands of the ghouls. If the Lone Wanderer follows her and successfully defends her from the ghouls, Millicent will stay in the first maintenance room found along the tunnels.
If the Lone Wanderer decides to deal with the "Tenpenny Tower" quest by killing Roy Phillips and his gang before giving Millicent the love letter, then he/she will not be able to give it to her as the Lone Wanderer will not go in to dialogue with her, she will only tell him/her well done for dealing with the ghouls.
She cannot be shown the love letter if the Lone Wanderer has already successfully passed the Speech check meant to force her out of the tower.
If she is killed 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.
ps3 If you're 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.[verified]
ps3 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, but only one shot will be fired and as she is scripted to shoot multiple times she will just stand on the spot after that. [verified]
ps3 If you attempt to steal from her and are caught the 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. [verified]
ps3 Dealing with her without using the letter then failing to pass the speech check with Edgar will result in Edgar never leaving. The only way to complete the quest in that case is to kill the husband or to raid the hotel with the feral ghouls. [verified]
pc 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. [verified]
ps3 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. [verified]