Hi C.
I disagree with some of your previous advice that recommend putting your daughter to bed later or cutting out her nap. I have read MANY things on this topic because of some issues we had with our 2 1/2 year old (also when a new baby came into the house!) and here's what I found out. Ensuring your daughter gets MORE sleep will help her sleep better...seems counterintuitive, but it's been proven. So, if she is skipping her nap (or waking up during the night every few hours!), she is probably getting too LITTLE sleep which makes her sleep even less---a self-perpetuating cycle.
Here are a couple of website that I thought you might be interested in, which say that a 3 year old should be getting anywhere from 12 to 13 hours of sleep per day:
http://www.babycenter.com/0_how-much-sleep-does-your-chil...
http://www.slumbersounds.com/baby-sleep-patterns-info.htm
It sounds to me as if the new baby has her schedule disrupted. Perhaps her bedtime routine was altered when the baby came? Or perhaps she is just experiencing more separation anxiety because she is now "competing" more for Mommy and Daddy's attention?
Ensuring your daughter has a very clear, consistent bedtime routine, which allows her to wind down, will usually help. We always take a good 1/2 hour to put down our 2 1/2 year old, turning off all of the lights except for one small reading light, turning on his white noise machine (we bought one when the new baby came b/c we have a very loud house (cement floors) and every noise carries). We talk about all of the fun things we did today and how he now needs to rest so that he can have lots of energy for tomorrow's fun activities. We say that Mommy and Daddy are going to sleep, too, so that we can also have energy for the next day. We read him a few books in a softer and softer voice and are practically whispering by the time we say "OK time to go night-night, we'll see you in the morning. Mommy and Daddy are going night-night now too"...
Make sure your daughter gets that time all to herself, where possible, i.e. no baby in the room (much harder to do when hubby is out of town). She may just be craving some of her own Mommy-time or Daddy-time, if she's unable to get it during the day. In fact, you may want to make sure that she gets some one on one time during the day so that she doesn't use the night-time for that purpose...
I really like some of your other advice re: teaching your child about an acceptable time to come wake you up in the morning. I will probably need to implement that now that we are about to move our toddler from his crib to a toddler bed (yikes!). Re: your daughter, putting a couple of books/toys right next to her bed (let her pick them out the night before), so that she doesn't actually have to get up to get them, may keep her in bed while she is "killing time" in the morning, so that she may fall back to sleep. We have found that if our toddler first calls out in the morning, but has to wait a few minutes for us to respond, he will go right back to sleep because he is still in bed. Just a thought...
I hope this helps!! (sorry for the novel ;-)
D.