I asked about using a backhoe attachment on my Yanmar 226D and the dealer said he had seen more than one small tractor that broke something when the owner tried to use them with backhoe attachments.
Lay of the land and water flow are difficult to grasp over the internet. That makes it difficult to say what is most helpful to you or would work. So the following are only possible ideas to look at---
My impression is that a trencher will cut a deep but narrow trench, but may not necessarily divert your water flow. If you have a bunch of large rocks in the soil, then that points to a backhoe. But it could be that a little reshaping of the surface with a dozer plus immediate reseeding and strawing might help, too.
If you could post a picture, I'm sure folks would offer more suggestions.