Jacklyn..
My background is that I am a mother of 5, and raised 6 children. They are all more or less grown, but I remember those years of sleep issues.
There are several things to take into consideration. One is her age. About 3.5 years old, little ones begin to develop an awareness of themselves as autonomous beings. They are not YOU but an individual. This brings on (the physiological growth pattern of autonomy) some difficulties for them. They feel scared, and confused in addition to feeling a need to break away in small ways from dependancy. That said, night terrors, or bad dreams can emerge.
The other thing is that little ones are very sensitive to their parents' struggles. Investigate what you are going through. How's your relationship with your partner? How's your sense of self? (with little sleep that can really get messed up). Also, with so much on your plate... a baby, a toddler, and one on the way, can make you feel pretty stretched and possibly scared.
One strategy I used (yes, this happened several times with several kids) was to calm myself with my breath, using the power of my heart. Breathe through the area around your heart, and try to release your own fears, anxieties, issues in that way. It's a simple practice, and not all that easy to do, but it does help alot. Done several times a day or during those night time care times is all you need to do. Your little one is reflecting back something to you, so calming yourself is crucial. If there are problems in your life, marriage etc. do your best to work on those... she just may calm down sooner than you think.
Taking naps yourself (everyone tells us that, and it's just about impossible to do with all that you have on your plate) is one solution that I finally used. It worked pretty well... and I didn't get much done during those times - so there was a downside to it, but I did have more clarity and peace.
I hope this helps.
K. (I'm a woman)