Tough spot. If you apply to allo rads during your intern year, you typically wouldn't start that residency until approx 2 years later since they are mostly set up to account for intern year before you start.
The other option is to do the intern year and try to land a rads spot that opens up for an immediate spot if you don't match DO derm...this would not be through the official match..it would be open because of a program expanding or from someone who was doing intern year at the same time as you who decided not to go through with their rads spot.
The better strat is the first one and find something to do in the intervening year...research or something I suppose. I think there are some categorical rads, but you would not have to do the intern year to begin with for those...but you could start right away. Either way, if you end up in rads, you will have probably 'wasted' a year (unless you don't go through the official match and find a spot as I mentioned in paragraph 2).
If you apply to rads year 4 and get in, you are bound and essentially unable to apply for DO derm your intern year.
If I was in your spot, I'd probably apply Allo derm and prelim years 4th year. If you don't get a derm spot, apply DO derm and rads during intern year. If you get DO derm, celebrate and move on. If you get rads, you have a year to take off to celebrate before you start rads.
I'm not familiar with what DO derm programs require, so I can't answer that part of your question. Best o' luck.