Linear and non-linear approaches can both be good! It just depends on which way you prefer - and on how much rewriting you can stand to do. If you're planning to publish, I think it would be very very difficult not to have the ending planned out in advance by the time you get your first book published; once it's out, you can't go back and change anything! If you realize you really messed up and now the plot you've discovered will be really broken and difficult to pull off, too bad, you're stuck with it. Before publishing, though, you have as much time as you want to rewrite and fix things! I personally prefer beginning at the... beginning, and writing and writing until I get to the end. It's much easier that way to have natural character and story progression, as you're writing linearly and adjusting as just the right speed! Too, you don't run into the problem of changing something early on and having to change it later, too, because you haven't even gotten to the later part yet. I also find that jumping around has the problem of sort of excusing the boring parts! If a part's boring when you're writing non-linearly, you just skip it, and eventually it becomes a big problem where you just avoid that scene for ages. If you're writing linearly, you have to write the scene so that you can get to the interesting parts; it's motivational! Some people have a really exciting scene that they're dying to write, and that keeps them writing everything before that so they can get to the scene, instead of just writing it immediately and then losing steam with everything else! Non-linear story writing has its own advantages, though. It tends to be easier to plot and piece things together, because you're not trapped in old stuff - you can just toss a piece out and write a new version if it's bad, because all the jumping around tends to create a lot less tangling - you can divorce yourself from the writing more easily, and take it apart, because you started with it being taken apart. It's kind of like if you're building a house and suddenly realize you want to change something about the bricks! If you were just building small pieces first and making lots of plans and seeing what everything looked like before putting things together, you could just do new pieces with the new bricks! If you've already stuck everything together, you'll have to take it all apart to change how the bricks are. And if a part is hard, you can just drop it for the time being and focus on something else! So sometimes that makes it easier to stay interested in the story, since you could have less trudging through. Also, last November I wrote myNaNoWriMo non-linearly as an experiment, and I found that although I was jumping around a lot in the beginning, I eventually went back and finished all the dangling chapters, and then I ended up with everything sorted out and was writing linearly again from there! It was also neat writing later parts and realize "oh, I should do that over in this earlier chapter so that this makes sense!" and then I'd know what to do with the earlier chapter and I could go back and finish writing it!
Relating to your particular story - if the child part isn't as interesting to write, are you sure it's entirely necessary? It seems to me that the parts that are less interesting to write and read tend to also be parts that could be dropped or heavily edited! If you're supposed to read the child part first, are there things you could change in the teenager part so that that's unnecessary? Alternatively, what is it about the teenager part that makes it more enjoyable, and could some of those things be applied to the child part? Is she just more interesting as a teenager? Does she have a more exciting adventure? Do you like the other characters that she knows as a teenager better than the ones she knows as a child? It can also be easier to write teenagers in general, just because being a child was a longer time ago, and it's a lot harder to know how children act and think and step into the character of one! I've found writing children characters comes a lot more easily since my smallest sister grew into one - I'm very familiar now with how she acts and thinks, and even if my characters aren't the same, it still makes it easier! I can see how much she's learned in the years she's had, and which concepts she still struggles with, and how much practice it takes her to get good at things, and her emotional depth regarding certain things, and what she as a kid cares about! (She's kind of special in that she's always been extra clever and interested in the world, and extra empathetic, and she has tons more initiative and planning skills than a lot of adults, let alone other eight-year-olds. But she's still a kid!) Maybe you could think about if that's a problem, too, and figure out if there's any way to interact with kids a little more and see if that helps!