give is a double-object verb: the direct object is WHAT you give, and the indirect object is WHO you give it to. If the word order is verb-DO-IO, a to is required. If the word order is verb-IO-DO, no to is required.
I gave a book to him
I gave him a book.
When you use the verb within a relative clause the direct object is at the front of the sentence, so either form is acceptable:
the best advice that parents can give their children is....
the best advice that parents can give to their children is....
This NGRAM shows that the version without to is more common.
Note that the idiomatic usage is to include the word can. This suggests that it is possible for parents to give this advice, rather than that they always give this advice.