Why does Mae Tuck travel to Treegap in Tuck Everlasting?

Mae Tuck travels to Treegap to meet her sons.  The Tucks have an arrangement whereby "every ten years, first week of August, they meet at the spring and come home together so's (they) can be a family again for a little while" (Chapter 10).  Angus Tuck, Mae's husband, would prefer for her to wait for their sons to come to them in their little cabin deep in the woods, but Mae is excited to see her boys, and insists on taking the horse and going down to the spring at Treegap to meet them.

During the long years since they have discovered the secret to everlasting life, Miles and Jesse Tuck have gotten in the habit of living life on their own.  As Mae Tuck explains to Winnie, "the boys don't be home very much...they go different places, do different things...work at what jobs they can get, try to bring home some of their money".  Unfortunately, they can't stay in any one place for very long, or else "people get to wondering".  The fact that the Tucks will never grow old and will never die leaves them in a very peculiar situation, isolated from the world and the natural cycle of life.

Mae Tuck has gotten used to the way things are, while Angus Tuck has not been able to come to terms with it.  Although it would seem that living forever is a wonderful thing, the Tucks have found that there are grave drawbacks to it, and have kept their condition a secret for fear that others will find out about it and seek it for themselves, only to find out too late that it is not all that it seems.  It is for this reason that Angus Tuck wants Mae to wait at home for the boys; if she goes out to Treegap, she runs the risk of being seen.  Mae, however, cannot wait to see her sons, whom she has not seen in ten years, so she goes out to Treegap to meet them (Chapter 2).