Dear sir/miss,
I am interested in your project and i understand what you want. I can easily meet your requirement as i am web designer and developer and can easily make it work. You want to show submit button if both like button is clicked if not than don't display the like button. If any one like is missing than show the missing one after like button is clicked than only show the submit button. I got your idea and i am ready to start the project right now. I will use ajax, javascript and php to make it work. I hope you will be available on chat for more discussion. Looking forward to work with you.
Regards
Sunwake