I don't know when you are due, but I wouldn't tell a 4-year-old (especially who isn't at your house very often) about the baby until you are pretty far along. 9 months is a LONG time for a little one... even three months is a LONG wait. We generally tell our kids around 6 months into the pregnancy, and it is still a long wait for everyone. By that point there is physical evidence that helps it seem more concrete-- my belly is bigger, they can hear the heartbeat, they can feel the baby kick, etc.
We also always tell my step-daughter's mother at a time when my step-daughter is with us. In our case we do it by email (our custody situation has always been such that she will definitely read the email before she sees her daughter). That gives her the opportunity to have whatever reaction she is going to have (we've always assumed she is not jumping for joy) and then compose herself before she hears the news from her daughter.
I think any "big sister" books would be appropriate for half-siblings, you don't need one specifically about your specific situation. Then just be open to talking about how things might change and how they will also stay the same in a lot of ways.
Some kids find it helpful to go to doctor or midwife appointments to hear the baby's heartbeat, see pictures of what baby looks like, etc. My midwives have all been great at talking to kids about babies and birth in a straightforward and age appropriate way. Of course that depends on your practitioner and whether or not that seems like something that would be positive for her.
It might also be helpful to make sure there are dolls and baby props around so she can do baby-related play if she wants to. Sometimes kids work out confusing feelings that way, or they find ways to talk about things that are confusing them.
I think it is great to involve kids in the planning and discussion, but if we go too overboard it can freak some kids out and make them anxious. I think being matter-of-fact, open to questions and concerns, having resources available if they decide to use them, and watching for signs of stress are a good way to go.
Parenting four little monkeys (11, 8, 6, and 4) with the love of my life. Making it up as I go.