Depends on the laws of inheritance in the nation in question.
We have plenty of examples of titles merging with the Crown in English history, for example, where a younger brother is created Duke (usually Duke of York), and then inherits the throne because his brother bit the dust without legal heirs.
So...as a very general
, what would happen is, the son would assume the mother's title and become Baron <PLACE>. When his father dies (or abdicates), he will become Duke, and one of two things will happen.
the Duke effectively rules in his own right (that is, he has no king/grand duke/etc. above him), then the Duchy he rules would most likely "absorb" the Baron title. The Barony formerly attached to that (now-eliminated) Baron title simply becomes another part of the land ruled by the Duchy. As mentioned, this happened repeatedly to the Duke of York title in England, merging into the King's lands.
2. If the Duke does not
rule in his own right--if he is a vassal to someone of higher rank--then the two titles would most likely stay completely distinct. The son, upon inheriting the Duchy, would thus be simultaneously a Duke and
a Baron, because those two titles have separate
contracts with the King(/etc.) that is their liege.
More or less, if the person who has or inherits a title is, or becomes, the same
as the person granting that title (e.g. the King/Queen grants the titles to Dukes, Earls, Counts, etc.), then the title is simply absorbed back into the Crown--in effect, you cannot be a vassal to yourself
. But you totally can
be vassal to the same monarch in more than one way.