

If not for Lwaxana, Odo would have never told Kiera how he felt about her, probably would have left the station and rejoined the big puddle much sooner, and as a result would not have been in a position to get the help he needed to prevent the genocide of his species.
And while Deanna certainly has issues with her mother, it is plainly shown that she has a relatively open and frank dialogue with her mother on a regular basis. To say “that Deanna only talks to her mother when pushed into it” is simply false.
No, the question was “How do you [prove that your from the future]?” You laid out a scheme, which you are likely not capable of doing, especially because you missed the bit about the terrifying complexity of that particular proof.