My sister in law had a doctor at a hospital she didn't like so when she had her son she went to a different hospital and they sent over her paper work there without hesitation. Any hospital will take you for health and safely reasons.
No you won't get in trouble they have to see you if you go into labor they can't just send you away BUT the hospital you told your ob tou would deliver at and if you registered there It's easier for you and baby to go there instead since your doctor would have sent the hospital your medical records :) and they would know who you are and all your info like blood type and so on just in case
What you can also do that i will be doing is ask for your medical records when your 37 weeks and they seal it in an envelope so when you go into labor u can take it with you to the closet ER good luck with everything
I have a regular obgyn but I've had 2 of my kids at a different hospital then where my obgyn is I do believe you can choose which hospital u wanna go to :) hope this helped