Must be three strand. It happens. The only advantage of three strand is price.
Used line can be re-spliced without losing any more strength than you would with new line (your BS will still be lower than new line, but the percentage you lose splicing it will remain the same with used vs. new). The problem with splicing used line is it is a lot more difficult to do.
Dock lines are cheap enough I'd just replace with new double braid nylon, or better yet - buy a spool and splice new dock lines to the lengths you want them. This way you can rig a set for your own slip with eyes on each end, to the exact length you want them, as well as an onboard set for traveling - and still have enough left over for a new double braid anchor line.