Dual purpose bike rack - seeking recommendations.

As SoundGuy suggests, put a receiver on your trailer and you can put most any bike rack you want in that receiver (assuming there is clearance between it and your tow vehicle, etc).

I have a Yakima RoadTrip Bike Rack (four bikes) that I've used on my motorhome and it works very nicely indeed and is quite sturdy. There are any number of other good bike racks made, of course.