You have a tough situation.
I think you are on the right track as you examine your options and set proper expectations.
One challenge I see with you moving to the east coast is that you will create a lot of disruption, esp. if you take a Full Time program:
1. switching jobs for your wife
2. leaving her sick mother who she feels close to or a strong need to be nearby
3. no income for you if FT program - that will be a change
4. possible marriage/etc - change as well
5. moving and relocating, finding new place to live, getting used to the neighborhood, city, climate, etc
I am very far from being a relationship expert, but I think if you move to the east coast, you will lose your GF - it will be too much change for the two of you to adjust and save the relationship.
Since you are committed to her, what if you wait for your application results - see if you even get into the East coast schools to start with. If you are really set on east coast and it is a good school worth moving for, you may have to compromise and defer your enrollment by 1 year or 1 semester and move later on - showing your commitment to your GF. She will always appreciate it and you will feel better too.
As to career changes and FT/PT programs - PT is indeed harder for career changes. most of your classmates will have jobs with their current companies and will be working towards a set career plan, whereas you will be on a new path, looking for a new job. I think PT program is not designed to re-define you, rather to improve and build on your existing experience. You may ask the Career Change question to the admissions at the schools you are thinking about or possibly the PT students at those programs, if there are any events like that.
I think ideal option for you is to get into Stanford FT program (easier said than done).
Second best option is Stanford PT or wait a year and move to the East Coast FT program
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