It is very normal for you to be emotional. I think it's OK to let your children know that you are sad. Focus on the positives but don't overdo the "how much fun you're going to have." Admit to the sadness. Do let them see that you will miss them and allow the 4 yo to talk about the change, both the good and the bad. All of you are feeling sadness and anxiety. This is an opportunity for emotional growth. .
I've found that having an adult with whom I talk over my feelings helps me put my adult worries aside so that I can help my child express hers. By talking with an adult I'm less likely to scare my daughter with adult worries and concerns. With children this young they may only need a few minutes of reassurance from you that not only is this a new adventure but it is also a sad one; that you'll miss them and be so glad to pick them up after work.
If your 4 yo is the verbal sort who asks questions give her time to do that. When she's sad give her a hug. Tell her you know she's sad and it's OK. Then do something light hearted and fun. The 2 yo may not understand what's happening and therefore may not be upset until this actually happens. That's OK. This is where leaving your adult anxiety out of your interactions is important. He will pick up on your anxiety and become anxious but not know why.
I think it's good you're starting daycare before you start work. You can stay with them for longer. Will they be at the same place? If not, I suggest dropping off the baby first. Let big sister be a part of getting him used to the place. Let the 2 of them play together for awhile.
Follow the lead of the caretaker as to when to leave. Actually I would talk with them before you take the kids. I think it's important to give our children support as they get used to new surroundings. I would insist that I was going to stay for awhile. If the caretaker knows that you're going to stay she may have had enough experience to know when it's a good time for you to leave and help make the transition.
Since you have a week to make this transition I suggest that you stay with them as long as you want the first day and then take them with you when you leave. Perhaps make the amount of time you stay shorter until on Friday you don't stay for long at all.
My granddaughter started day care when she was 3. From day one she seemed to not be very anxious when Mama or me leaving. The workers got her involved with other kids climbing on the indoor jungle gym. Sometimes she would cling. I would reassure her that she was going to have a good time and I'd be back later. I had enough time to stay with her for 10 minutes or so; long enough for her to get involved in play.
She clung and was more teary when she started kindergarten. The teacher was great about getting the kids started doing something.
My grandson always cried when I left. I stayed with him for an hour or so the first day. I left once he was involved with toys/kids. I did give him a hug and tell him I'd be back later. He'd cry and the in-home daycare "mom" picked him up and walked me to the door. Then they both waved bye. He was always having fun when I returned at the end of the day.
Assume that they will be OK. Show confidence in them. Then cry when you get out to the car.
I think that you being at home with them for as long as you did will make it easier for them to transition. They are secure in your love. As you said, it may be harder on you than them.
One of my mother's sayings is "this too shall pass." That became my mantra when I was upset.