Pan and Trunks Get Married
-or- Have a Child -or- Have Vegeta Jr.
If we go by the logic clearly expressed in the final episode of Dragon Ball GT, this is impossible. Goku Jr. is Pan’s great-great-grandson — this we cannot dispute. Therefore, if Goku Jr. is her great-great-grandson, it seems largely impossible for Vegeta Jr. to also be her great-great-grandson, as well. It is quite obvious that after GT‘s normal continuum ends, Goku’s and Bulma’s/Vegeta’s families either have some sort of “falling out”, or just normally lose contact with one another (as Goku and all of his friends tend to do over the course of the series). Vegeta Jr.’s mother does not recognize Pan, while Pan recognizes the Capsule Corporation logo and its connection to Bulma. Also, when Vegeta Jr. appears in the Budōkai ring, Pan is surprised to see someone who resembles the elder Vegeta (clearly meaning that she has not had any contact with that family for at least as long as the child has been around; a great-great-grandmother probably would not be so disinterested in her own descendants).
Vegeta Jr. is not necessarily Trunks’ progeny, either, since Pan and Trunks are relatively far apart in years (roughly 12-and-a-half, going by Trunks’ birthdate late in Age 766 and Pan’s in mid-779). It seems more logical to assume that he is Bra’s great-great-grandson, and not Trunks’. His mother’s teal-colored hair, the same as both Bulma and Bra had in the anime, seems to lend credence to this theory; however, since we do not know the dominant / recessive genetic characteristics of anime hair colors, we cannot completely rule out Trunks, either. Regardless, Pan has obviously not been in contact with them for many years, to have to take a minute to recognize the extremely Bulma-like woman who sits down next to her. Of course, you could make the argument that Pan could be going senile in her old age, but since she recognized all those other things from her youth, that seems highly unlikely.