S.H.
stop the snacks & juice! Then stand firm at mealtimes...start with a quick drink of milk - no juice!- & then she has to have 3 good bites of each food item on her plate before she can have the milk again. Reward her with a small treat - a cookie, etc - if she willingly complies with this process.
I know this sounds harsh, but she's got you over a barrel right now! You're worried, you're desperate.....& you need to take control. Oh, & the 3 bites comes from her age.....just like one minute for each year of age for timeout....it's a reasonable amount.
Hopefully addressing these eating issues will help straighten out the sleeping problems. Good Luck.