I agree with hisannabelle 100%. You cannot force someone to do something if they wont at least try, and it honestly (dont take this offensively either, just my pov), attempting to force her into submission seems like a power struggle to me, like you both are competing for it symbolically. Personally I'd stop that and give her an ultimatum if she said no.

I'd say 'Im not hearing a yes, so im out the door."

Sticking to your words (even if you dont like it yourself) is a must. If she really Wants to have you dominate her, she needs to ask for it and submit Willingly. It will not work with her challenging and goofing off and playing games. I think a talk is in order to really discuss what she wants with none of this "you have to force me to submit". It doesnt work that way. Even as a Domme, she should know it doesnt work that way, and as a sub she needs to learn its a two way street. You can only go so far when she is not granting you all the power she claims she want you to have.

A Dom is nothing without the power the sub gives Him.