If your son is allowed to do those things, why isn't she? She's part of your family now. Can you imagine - your son looking at the cards "I see Uncle Barry remembered you this year". Daughter in law gets up to take a look, and it's suddenly rude, impolite, not done in our culture.
It's not down to cultural differences or upbringing - it's a peculiarity of your family who can't bring themselves to accept her.
If you discussed this with her husband, he might say that you're petty and your ex petulant. Why not start treating her as a daughter instead of as an outsider?