Masters in education during physics PhD How feasible would it be for a PhD student in physics (who is interested in teaching high school after their PhD) to receive a masters in education from the university they are receiving their PhD from?

I would think that at least during the first 2 years of a PhD program, before qualifying exams when you are taking courses and being a TA, this is in no way feasible.

What about if you had permission from your PhD research advisor to do so during the later years of your PhD, when you are only doing research and have less (or none if you're funded) TA duties?

How competitive would getting into the school's masters in education program be? I would think that being a PhD student there would help.

Would being a current PhD student help in receiving scholarships to alleviate the costs of the masters in education?
Seems to me like a long shot. There are a lot of obstacles. But first, few secondary schools require a doctorate to teach. So, what is your real goal? The doctorate? Secondary teaching? 

Next, you won't have much of a life if you try it. Think 80 hour weeks for a couple of years. A doctorate doesn't often get easier after you pass comps. 

Just the scheduling will be an issue. If you are taking courses in two departments, they won't coordinate class times to make it easy for you. 

But, perhaps, the biggest obstacle is fining an advisor who thinks it is a good idea. "Where is your commitment?" 

As for being competitive for admission, I think it might be a minus. Again "Where is your commitment?" 

Costs might be an issue or not. A doctoral student in the US normally has funding sufficient to live, but it normally comes with duties that take time. Tuition is normally waived. But it might not be for the other program. 

But, it may be possible (just) if you want to completely set aside all other concerns for a couple of years. Hard, though. 

Most secondary teachers with degrees in field, get their education credits over time through continuing education. It is the normal practice in the US. Finding time for a course or two in field-related pedagogy is a more modest goal, and more feasible. But still not essential, as few people actually do that in the US.