What a very normal and natural, a little tougher than most, and a very challenging situation you have with your very delightful bundles. Yes, you are right... you've already proverbially pushed the toddler off your lap; it may not be such a great idea to push her out of your bedroom too right now. I don't see it making things better. You might want to try some musical parenting though (like musical chairs). Sometimes dad and toddler are in this room, and mom and baby are in other, and other various combinations as the needs arise.
Your two sweeties have found a way to get the amount of attention from you that they each need. All you need to do is learn how to live without sleep : ) If there’s anyone around offering to help, take them up on it and squeeze in a nap with baby.
If baby cries while with dad as you put sis to bed, I see that as mostly OK. The baby is not being abandoned to cry unanswered, she's getting to know dad. The two of them will bond more and work it out between them, and in the meantime, dad is providing acknowledgement and empathy for baby's cries –- a very different thing from "crying it out" alone. Maybe he and baby can go out of your earshot, to reduce the stress on you for a bit, to be sure baby isn't seeing/hearing you and being reminded of what she's missing, and to allow toddler to be thinking of just you and herself for a time. At this very young age, the baby might "like" dad better if he's wearing a t-shirt that is strong with your scents. It's a little confusing bit of trickery but it could be calming for baby and she'll get the two of you straight soon enough. On the other hand, it might just remind her of milk and be more frustrating. It's worth a try.
For the baby, do be sure that you have her sleeping in daylight and natural family noises when she's sleeping during the day, and have it very dark for night sleeping. Of course, if you need to be up with your dear baby at night, you don't want to be in pitch blackness but do try to keep all lighting dim during the night. Be affectionate and respond to all her needs and cues, but maybe be a little boring at night, and more fun during the day.
Some moms find it very helpful for the toddler to tandem nurse along with the baby. You could invite her. Since she's already left the breast, she may only nurse ceremonially, but it may give her opportunity to bond with the baby, to bond with the new mother-baby dyad, and to return to some very special feelings with mom.
There are several nice books out there about dealing with siblings. I wish I had good recommendations for you but I don't. How about other moms out there??
If you can get the toddler involved at all in baby-care or just baby-care decisions (gosh she seems really hungry, just like you used to get when you were this small, what should we do?) that would be great. Create warm-fuzzy sister adventure stories to tell at bedtime and other times for sis to imagine what it could be like when they are both a little older (maybe it can be a self-fulfilling prophecy). Tell her of all the values of being an older sister. Confirm as often as you can how special your toddler is to you and daddy, and try to create a specialness of the baby to her. I've heard of families giving a special doll or similar "gift from the baby" to an older sibling. Sometimes it might just provide the spark that's needed.