Conflicts come in two general categories. There is external conflict and internal conflict. One internal conflict in this story is the internal conflict that Winnie struggles with throughout the story. This conflict is whether or not she should drink from the magic spring water. It will make her immortal, which sounds great to her, but the Tucks strongly advise her to consider the repercussions of such an action. Winnie also struggles with her own desire to go out and do great things. Her home life is a very constrained and oppressive home life. She feels like she is constantly under close observation from her family, and she longs to get out from that environment.
"See?" said Winnie to the toad. "That's just what I mean. It's like that every minute. If I had a sister or a brother, there'd be someone else for them to watch. But, as it is, there's only me. I'm tired of being looked at all the time. I want to be by myself for a change."
Externally, the main conflict is between the man in the yellow suit and the Tuck family. He wants their secret, and he wants to market it for a profit. The Tucks absolutely do not want that to happen. Winnie winds up in the middle of this conflict, and it eventually turns violent when Mae Tuck cracks the man in the yellow suit in the head with the stock of the shotgun. Mae is arrested for her actions, and this starts another conflict. The Tucks and Winnie have to figure out a way to save Mae.
One conflict is man vs. self. This conflict is Winnie's conflict. Should she accept the offer of immortality or not? Only she can determine that for herself, and she struggles with it quite a bit. The reason that she wants to take the immortality is because she wants the freedom that comes with it. To go off with the Tucks, she would not be under the rules and regulations of society. She reveals this desire early on, when talking with the toad:
"It'd be better if I could be like you, out in the open and making up my own mind."
However, what she comes to understand is that too much freedom is dangerous. Without limits, there is danger. Also, without a limit to life, joy loses is power. Winnie comes to understand that love and joy are so intense because of the mortality of humans. We have a short time on this earth, and must cherish our happiness. Take away time, and you take away happiness. Jesse's parents make this clear to her, and she bases her choice on their advice.
Another conflict is man vs. man. The greed of the stranger in the yellow suit threatens the Tucks and Winnie. He wants so much to have immortality that he is willing to reveal the Tucks to society. They would be victims of any number of strangers seeking to have and to understand what has happened to the Tucks. This is why Mae is forced to murder the man, ending the conflict with him.