A: Respected Brother/Sister in Islam
As Salaamu Alaykum wa Rahmatullahi Wa Barakaatuh
Haamidaw wa Musalliyaa
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
Shafiq Jakhura (Mufti)