I agree with jpsdad that your water appears to be nutrient rich.

Some other alternatives are to plant some desirable shallow-water plants in areas that do not interfere with your swimmers. Those plants will take up a portion of the nutrients from your water. (If your cover over the liner will not support rooted plants, I believe some people on the forum have had success with plants in submerged plastic planters.)

Another option is a floating island of plants.

Here is a link to a recent thread on floating islands.

Floating Island

My other observation is that swimmers love docks. Perhaps you could put a dock in the middle of the pond and combine that feature with the floating island for a dual-purpose project.

If you (or more importantly, your wife) think that is too ugly, then you can do a "landscaping" type styling on your pond with features that would help the water quality (for swimming) and make the pond more visually attractive.

Good luck on your pond!