Which one is right:
Enjoy with family
Enjoy with the family
They are both correct. If you want to specify a certain family or certain family members you use ‘the family’. Whereas ‘family’ is used to talk about family in general.
For example, somebody might say to you ‘enjoy the holidays with family’ they probably don’t know your family very well or want to talk about your family as a whole rather than certain members of your family, like your nuclear family.
Whereas ‘enjoy the holidays with the family’ is addressing your specific family members, the specific family members you are spending the holidays with.