M. - My older child (2 year's difference) tends to act difficult when he feels like he is a "task." For example, in the mornings when we're getting ready for school, if I get him out of bed and go straight to changing him and leaving for school, he fusses the whole way and then doesn't let go at daycare. However, if I take the time to cuddle with him for a few minutes when he gets up, then make time for breakfast with him, he feels important and loved and has a much better day. Although this is not your direct problem, I suspect that "being a task" may be affecting your daughter at bedtime. As others have suggested, try carving out some time with just your daughter - whether it be your husband or yourself - before bedtime. You may find that her bedtime routine gets longer now that baby is hear, but a routine for her at this age is so very important. When all else is changing and hectic in your lives, routine and a reassurance of her mommy and daddy's love can work wonders. If you are able to offer her this time, I think you will see great improvements.
She may be too young to be able to communicate her feelings verbally to you; remember that she probably wants to tell you why she's frustrated but can't.. that can spark even more emotion in her, magnifying any issue even further. We had some success in sitting down with our son after the bulk a tantrum had passed, taking deep breaths with him, and trying to explain logically what was happening. We weren't angry with him, but he's a big boy and needs to sleep in his room. Mommy and Daddy's bed is small, and we want you to have room to sleep well in your big-boy bed.... When tantrums ensue, it's often a good bet to offer them a quiet hug of reassurance after it's all said and done. This is not to condone the tantrum, but rather to remind them that even though they and/or mommy and daddy were upset, mommy and daddy still love them.
Also, try to get sleep during the days. If friends/family are an option for you nearby, or if there is a mother's day out, send your daughter with them for a couple of hours (perhaps even one hour) and try to get some down time / nap time with your son. If this is not an option, or if you work full-time, perhaps you have an opportunity to cat nap with the baby in the early evening before bedtime, letting your husband spend some alone time with your daughter.
Best of luck. Although it may be of no consolation right now, this too shall pass.