tree in your last pic looks like a red bud. I don't know if they live in your zone or not, but I think that is what it is, hard to tell from the photo. Honestly you have quite a problem here, I can imagine that during periods of heavy rain (which you do get sometimes?) this slope is steep enough to call a hill... it is going to wash all kinds of stuff into the pool area. I don't think any wood mulch is a good idea because it will float as well. You may consider putting in some large rock to help hold the soil in place and then plant in the pockets that are left. The best thing to do is find a local nursery/landscaper that is more familiar w plants in your zone and the erosion issue. Around here some people use a lower growing juniper evergreen to help cover the ground in slopes. I am thinking smaller plants will not root deep enough to fix this and it will still wash out ?
