First of all, there is no point in pursuing a second Ph.D. degree in physical education when you already have one. If you are going to pursue your second Ph.D. degree in some other field, it could be understood because it makes sense. Many do it for a career change. By pursuing a second degree in a different field, your career opportunities increase. Thus, I would advise you to seriously consider once again about your choices and make the decision wisely.
You are allowed to pursue a second Ph.D. degree in a different field from the same as well as another university. Lots of people do that. Also, if you are sticking to physical education, you need to enroll in another university.
If you want to pursue the second Ph.D. in the same field, be ready to invest 3 more years in pursuing it. Instead of that, you can start your career as a coach, physical education teacher or fitness instructor.