She shouldn't even be able to beat her father in a straight fight, so unless the author decides to pull something out his ass... which would be uncharacteristic, she'll have to use less direct means. Whether that means shaming her father into submission over treating her this way, teaming up with Jun (which will likely result in capitulation anyway, since the father doesn't want her to actually hate him, she just left/played up the silent treatment before his guilt overpowered him.), or somehow convincing Jun to ignore the challenge (Unlikely, a man traditional enough to ask for a daughter's hand in dogeza will have strong traditional values of age and seniority, which I find people seem to ignore in favour of bashing Jun for being weak willed.)