Of 2 am soaps and late night movies

I am now the expert of what all comes on TV at 2 am in the night, courtesy A. A sleeps peacefully throughout the day and is wide eyed from 11 pm onwards when the rest of the house starts shutting down. 11 am t0 4 am is my official time to look after her since my mom sleeps at that time, so after many unsuccesful attempts to switch off the light and put A to bed in the bedroom, i give up, come to the living room, switch on the TV and mindlessly flick through channels. The preferred ones are Star World and Star Movies since those are ones with subtitles which can be watched on mute, and now i'm up to date on eposides of Prison Break (never heard of it before), Sons and Daughters and other such serials. Miss Friends though- thought there was a 12 am episode running earlier.

The hubby, who gets his daily 10 hours of sleep insists i should keep A awake more during the day. Frankly dont see how that is possible, since she is too young for us to distract her with some toys or a story. She only cries when we try to keep her awake and then we're forced to put her to bed The hubby also suggested putting water on her or giving her a cold water bath!!!! after some unsuccesful attempts to keep A in a sitting position to keep her awake - she slept through that as well!
My cousin, who had the same problem with her daugher, suggested giving a sleep medicine in the night which would break the cycle once and hopefully change it for the better. But i feel A is too young to give such medicines, so will go back to the mindless surfing of channels for now.
Btw can't beleive there are so many teleshopping channels suddenly- rather many channels only have teleshopping at 2 am in the night- do people really shop at this time?