There’s a closed Facebook group called Physician Mental Health whose goal is to allow physicians to discuss their mental health issues and struggles. There’s an option to post anonymously if you choose. This might be a good place to post your question and perhaps find comeraderie.
Personally, I’d go one week, but not both and not disclose where you are going, but be sure to let them know way in advance that you’ll be missing part of a Friday. Then be fully present and impress the hell out of them during the time you are there. It’s truly a shame that the medical community can be so intolerant of mental health issues, but that’s the way it is. Huge kudos to you for getting the help you need now.