A lot of people working in children's books /illustrations came from an animation background (Jon Klassen, Christian Robinson, Claire Keane, Molly Idle, Pascal Campion, just to mention a few). I almost think it might be an advantage to study animation for doing children's books.
Sometimes, it is really hard to know what you want to do until you do it. My experience is to pay attention to how you feel when you are doing an animation project, compare to doing an illustration project. IF you have done a short animation and you have made a children's book yourself. Then you can compare the process, which one do you enjoy more.
Both animation and children's book is a time consuming process. I think the only way to not burn out is to really enjoy the process of doing them.
I hope you will have fun with whatever you choose.
And remember education does not define your profession. You can always change your mind. And if you have worked hard, nothing will be wasted :-). I studied graphic design for my BA, and interaction design for my MA, worked as an interaction designer for about 10 years. Now I am doing children's books. All my past experiences are very useful for me regarding making art, and also dealing with client relations.