The above advice is great. I'd add, start "camping" in your RV/tent in the driveway at home. Do that for several months before true camping season begins (if your weather lets you) so that you have had time to adjust to the new lodgings before you start taking it to new places. Getting used to the normal movements, sounds, etc. that occur before you encounter them in a strange place can reduce potential anxiety.
With the potential of emergency room visits, I would suggest not getting an MH. With an MH, you would have to basically take apart camp in order to leave for the ER. A tent or TT would allow you to just hop in the vehicle and get to the emergency room - leaving the camp set up for your return.
Knowing your triggers can give you a better idea on what your tools will be. For example, if feeling vulnerable is a trigger, a tent or tent trailer or hybrid might increase that feeling, whereas a hard-sided RV could help minimize them. Whereas, if feeling boxed in is a trigger, then the hard-sided RV could be a worse choice.
Start close to home. Find the closest campgrounds and spend your first season at those getting used to the whole thing. This will allow you to easily "jump ship" and go home if it's too much. Keep your campsite simplistic. Don't have tons of things set out all over the campsite. Everything that is out will have to be put away before you can go home. Make it easy to call it quits - you'll do more damage to yourself and your family by making it difficult to pack up quickly and go.