A man is a Shari Mahram for his daughter
inlaw. Hence, it is permissible for his daughter-in-law to travel with him.
However, due to the fitna's and evils in our times and the number of incidents
that have taken place, it is advisable for the two not to travel alone together
especially when they are both fairly young. If indeed, they have to travel
together, care should be taken not to be in seclusion with each other where
Shaitaan and Nafs could tempt them towards evil.
And Allah Ta'ala Knows Best