To me it sounds like you're putting a lot of pressure on her, probably without realizing it. When I read your post, it brought me right back to coaches I've had over the years that took the fun out of everything. I was a definite daddy's girl growing up and would get pretty stressed out about not wanting to disappoint him. He learned pretty early to not push, because I was hard enough on  myself. Is she paddling for herself or because you want her to not waste her talent? Let her hang out in a ducky or raft if she wants to. Make it fun, she's only 10. If she really wants to kayak she will, but if she's not sure about it and you keep pushing, she'll probably not make it a lifetime sport and maybe even resent you.

Like someone else said, let her paddle with others she feels comfortable with. Ask her who she wants to kayak with and let her just have fun with you in the water instead of doing "drills". Play tag or follow the leader in kayaks or something, but don't make it work and drills. Just redirect your intesity to just being fun dad instead of coach, she'll most likely come around.