I just had my fourth baby 2 weeks ago, and my kids have never had any trouble with adjusting to a new sibling. I could probably have 10 kids and never have an issue come up, so we must be doing something right.
I think the key is keeping yourself available to your older child(ren). Paying attention to all of one's children is always very, very important, but especially when there's a huge change in the family dynamics, like the birth of a new little one.
Just this week I put an extra table into our kitchen so we could put a puzzle together on it. My older kids love puzzles, and so whenever I have a few extra moments in the day, I sit down with at least one of them to do the puzzle. Sometimes we talk quietly and sometimes we just work in silence. It doesn't matter as long as we're spending time together.
I still read to my older children, which I can easily do while I'm nursing the baby. It makes my older kids feel important, too. They love being read to, even though they are strong readers themselves.
I also let them help me with baby care. My oldest has little interest, but does like to occasionally hold the baby. My second-born likes to be heavily involved with baby care, and has even changed diapers. She's the only one who really wants to change diapers, so she's the only one who does. Children are very good at letting you know what level of involvement is just right for them. I would let your 3-year old hold the baby with you there, of course. You can pay her little compliments about what a good job she's doing as a big sister, stuff like that.
Make sure you take good care of your own needs also. You'll have more energy to spend with your older child.
Perhaps you can encourage Dad to take your 3-year old somewhere special during the first couple of weeks postpartum, when you're still recovering.
It'll be fine!
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