How can a light just turn its self on????

we had a similar experience at our last house, i was always 'on the fence' about ghosts and hauntings although i believed in it there was no proof for me to be sure until we moved to that house. my daughter was between 6 months and 1 year whilst we lived there, she would act like she saw someone in the doorways and would smile and laugh, the house was generally cold and had a horrible feeling to it, things started moving, we started hearing noises and my daughter stopped sleeping at night shed wake up crying all night so we had to co-sleep and she was fine once out of her cot. there would be unexplained music bursting through the house that only i could hear once my partner went to work and it got so bad we had to move. we did end up finding out it was haunted by two old people and 'creatures' not human. someone had done a ouji board in the house before we moved in and let things in. not trying to scare you but something similar could be happening to your house especially if its effecting your daughter so much. is there any chance to put her in your room for a while to keep an eye on her and see if it gets worse? i was petrified to leave my daughter alone and only felt safe when she was in the bed with us at night. if it does get worse id consider moving, but could be worth speaking to someone to get the house blessed. good luck.