I've been off trying to find what brand/model of DVD drive is used in those two external drives you have. Sometimes a firmware update is needed when drives won't recognize the presence of an inserted disc, or think the disc is closed when it isn't, but you need to know exactly what drive you have before you can progress.
I couldn't find a MUSC brand drive in any of my searches. I found that Amazon sells Cocopa drives, but going through the reviews I found a very high number of complaints about them, and couldn't find anything about what was inside them. The unit originates in China. Complaints included many that were DOA, and many that wouldn't work in Mac or PC, and many that had stopped working after a short time. A reviewer said the "Instructions" were written in micro-print on a tiny piece of paper, and there was an offer to send drivers for the unit "if requested". The problem was there was no model or serial numbers on the unit or the box, and there was no address to send a request. Another customer said although it's advertised as a USB3 interface, his machine reported it as USB2. In any event, Amazon says "Currently unavailable. We don't know when or if this item will be back in stock. "
I invite you to read some reviews for yourself, at the bottom of the page HERE, but I'm afraid you may have bought yourself a lemon or two.