The DM is charged with making rulings on a huge variety of things that go on in the course of playing the game. You can make your case for why you think it should be a given way, and then await a ruling.
Once the ruling has been made at the table, the DM is right1.
During play, accept that and then press on as the other players wish to play for fun and are probably not there to watch an argument.
Once play is done for that session, you have reached a potential decision point.
Is this particular decision a deal breaker for you? Do you want to revisit it outside the time constraints of a gaming session, in a non-confrontational manner? If not, if mostly you are having fun, then roll with it.
In this case, you picked that cantrip with the expectation that you could do certain things, and have just found out that you can't. In a non-game time environment (or in a friendly email) present the PoV that your expectations were not met (by accident) and ask for another cantrip. Or, ask that she reconsider the ruling once you've explained your position. Your request must be unemotional and non-confrontational.
DMs do this for fun, not for pay.
Once you've re-stated your case, accept any follow-on ruling with good grace, pro or con. She does a lot of work to run this game for your group.
Peace between you two will benefit the whole table.
If this ruling is a deal breaker ... if this is a decision in a pattern of rulings that you find are consistently dashing your expectations against the rocks ... then you need to have a different (unemotional) dialogue with the DM:
Are you two playing the same game with the same expectations?
If you can't reconcile that, this table may not be a good fit for you.
Even if you don't always see eye-to-eye, there are some things that you can do. You can contribute some good faith effort to future decision points.
Without going through the eye-watering detail of the Same Page Tool, it's worth your while to look at spells that you are interested in adding to your spell book before you get to them. Likewise the spells you already have.
Do some homework, and a little forecasting. Try out some practice scenarios yourself. What would I do in X case? In Y case?
In an email or a conversation outside of a game session, present some of your ideas on how a spell might work beyond its obvious uses. A lot of DMs appreciate ideas raised and resolved before or after the gaming session where a non time-critical decision is achievable. (I sure did when I was running games during my early DMing years, and I really appreciate it now that I am running them again. My group has a lot of "how does this work?" and "I thought it worked like this" episodes).
You may be able to get her to "see it your way" a few more times when she's not under time pressure. Or not. However this dialogue plays out will inform your decision on whether this is a good table for you, or not.
Insofar as the interpersonal skills: the more non-confrontational you make your approach to her, the more likely you are to get her to see it your way on some issues, but you won't always get your way.
At the end of the day, the DM's rulings are the rule. She's got more than your fun to consider, she has the whole table's fun in her hands as DM.
Best wishes for continued fun at this table, or any other.
1 (PHB, p 6)
Ultimately, the Dungeon Master is the authority on the campaign and
its setting, even if the setting is a published world.