18 month old

Okay ladies i need some advice here i am a teen mother. I have an almost 18 month old little girl named Lillian and a 5 month old named CicilliAnna. my daughter lillian is a monster and it has gotten worse sense her father has been in and out of her life. She finds it utterly funny when mommy says no. and keeps doing it she likes to get into things when she knows shes not supposed to i understand she is just a toddler. i have tried putting her on time-out and she listens for about an hour and then does it again. she is very good, kind and gentle with her sister. although she does get a little rough but once cic starts fussing she goes sorry cici gives her a kiss and walks away. but she likes to hit and bite.
i need some advice on how to put a stop to it..
i also need some advice about getting her to sleep on her own. when i try to get her to sleep by herself she screams until she pukes. i made the mistake of letting her sleep with me as a baby being a new mommy and her dad coming in drunk alot i was always afraid he would fall on her so she slept in my arms. now it is very difficult being a single mommy of 2 baby girls exactly a year and 19 days apart dont get me wrong i love being a mommy and i love my girls it is the best job in the world. i just need a little advice is all.

my youngest is 2.5 and she still smiles and tries to keep doing things she shouldn't. We do time out between 5 to 10 minutes..sometimes it helps sometimes it doesnt. I don't have a problem with her sleeping by herself, but she was never with me in bed, there are cocassions when she falls asleep with me but I always put her in her bed. You may try that and see if she will stay asleep that way..For my oldest she gets irragular sleeping patterens very easy so for her age we do 4mg of melatonin is a natural relaxer about an hour before she is suppose to go to bed and it helps..it doesn't really put her to sleep but it helps keep her asleep so she isn't waking up in the middle of the night and throwing off her schedule. I hope that helps..