You cannot use the seatbelt and the harness together. It can cause many problems, yes. The seat will either fail, or it wasn't tested that way in the first place. Either way, you don't want her in that position.
How heavy is she? And she's on the side of your car, not the middle? You have the top tether done up (if she's forward facing)?
I'd double check you have the harness above her shoulders (for forward facing) or below her shoulders (if rear facing), and that the harness just passes the pinch test. You don't want the straps below her shoulders, and you don't want to be over tightening. The straps below her shoulders is wrong, but the combination of the two means she's very uncomfortable, and she's more likely to try to get out.
You can use discipline for her. Either positive or negative. For every trip she DOESN'T do it, she gets a sticker. For every 10 stickers, you go for ice cream. Or, every time she does do it, you take away a half hour of screen time. Or something, those are just an example. Maybe you promise a trip to somewhere fun, and if she does it on the way, you don't go to that fun place. That's both in one. If she doesn't, yay, she gets to go. If she does, boo, she doesn't.
Is another Britax an option? Let us know her height and weight, and we can recommend a seat for her. Britaxes start at under $200, so if that's doable, that may be the easiest thing. Either rear or forward facing.
This is a super common issue with three year olds, so don't fret too much. Know that it's developmentally fairly normal. Three year olds have taken being two and turned it into an art form. And that involves really NOT wanting to be restrained. In theory, we're the adults and we can outsmart them, but being three years into sleeplessness and 18 months into being pelted with WHY WHY WHY doesn't help our cause.
We've got your back.
Wendy