If I were you (or your in-laws), I would give it a try and see how it does. It may not bloom as much as it would in full sun, but with dappled sun it will probably bloom some and the blooms won't fade as much as they likely would in full sun. I have some clematis that face north growing up my porch rails and they definitely take longer to come up in the spring than those facing south, but once they do come up they bloom pretty well. I also have lots of clay and never fertilize with anything other than homemade compost as a top dressing.

A chain link fence would be a great trellis, so they could always ask their neighbors if they'd mind a non-invasive flowering vine growing through their trellis. They might like it, and if not then some sort of trellis (or woody shrub) would work.

Are there Clematis that are better in the shade than others? For example, are there any red clematis that are easy to grow in the shade? Having scent would be nice, too.

As for asking the neighbors, let's just say they are not friends with any of their neighbors, so growing it on the fence is not a good idea.

Paul

The pink ones like Nelly Moser will do better in shade than many. However, if the rose won't bloom, it is highly possible a Clematis won't.