Everyone had great words of wisdom for you! Particularly Jerri, who already said everything I would. From a fellow shared-custody standpoint, this is definitely challenging...but not impossible! I have had stepkids from ages 3 & 4, and now 11 & 13. If you set the ground rules now, she will understand how your house works as she gets older. Our situation is that we have rules, mom does not (and is not interested in coming up with a united front for both parents to present to kids). So we had to make it very clear that "different houses have different rules" and you will obey ours while you are in our home. This has worked fairly well. We have had to repeat it many times over the years. Set the expectations and be consistent with follow-through of consequences. If she does not want to eat, then she does not get to until the next meal (this is a rule for our own children as well as stepkids, and you eat what is served to the entire family, not something special - I am not a short-order cook!) I would get her into helping you prepare meals, choose foods at the store, and browse cookbooks to select recipes she can help make. Also, the bedtime routine. I work at home, often evenings - so bedtime is tough for us. When I make a distinct effort to do bedtime routines, everything goes so much smoother! This means a regular set bedtime of 8pm, and I will start teling them at 7pm, "one hour til bedtime", "45 minutes til bedtime", etc. to help them wind down. It also means a toothbrushing/potty time, storytime, tuck-in, butterfly kisses, eskimo kisses, lights turned down low for 15 minutes, then out completely. So we wind them down slowly. If I do NOT do this, they do NOT go to sleep, there are temper tantrums, etc.
A rewards chart for this age (at both homes if you can) is also useful (you brush your teeth - you get a star, you clear your place from the table - you get a star) which did work wonderfully for my stepkids as well. I have posted job lists and lists of what is expected (treat others with respect, obey your parents, no lying) from day 1 with my stepkids. They are well trained by this age, but before they were very old (even old enough to read), they also responded well because they KNEW that there was a written list. This seemed to be like the word of God in their minds and they never questioned it.
Also make time for fun. Simple things like cooking together, walks, time at the park...this is what she will remember when she gets older.
I will keep you in my prayers. If you can talk to Dad, try to present a united front. It is definitely easier! I would love to hear how this works out after a few months. Keep us updated!