can a father in law restrict her son in law to not to kiss her wife in front of their parents?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

Evidently, such matters are determined according to the common practice of the community; Muslim jurists held that ‘Custom or common practice determines, i.e. it is an accepted source of legal prescription (in the absence of relevant religious text).’

Based on that, if kissing one’s wife in front of her parents is regarded inappropriate in a given community, then the parents have the right to ask their son-in-law not to kiss her in front of them.

In any case, a husband should not kiss his wife in front of people. Kissing is an intimate action between the spouses that should be done in private, not in public.

Allaah Knows best.