Oh I think you're being distant enough, it's maybe even bordering on "cold and indifferent" so be careful. MWD says to detach in DR, but in other books she clarifies to LOVINGLY detach.
Interesting that the doc was worried about his safety. This tells me that they gave him that depression checklist to fill out and that your H indicated on it that he had been thinking about suicide. And not only that, but H must have ranked it pretty high since the doc wanted to admit him right away. I hope your H follows through and sees someone because he is probably going to need A/D's, and quickly.
What all this means for your R is a big question mark, so just keep up your DB'ing. If he starts A/D's it'll be 4-6 weeks before they fully kick in, and even after that there's no predicting whether it will make him more interested in the M or not. Hang in there and be patient!