My ultimate 2 problems are 1. my backyard and side yard just basically is unusable for a day or 2 after rain because of the water and 2. massive runoff is eroding the edges of my driveway, causing it to crack and I REALLY don't want to replace it if I can avoid it...

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only thing I can think of is to divert the water around the 2 problem areas... but I can't go the "easy" path as its fully blocked by my driveway (it has a "T" section that goes to a separate garage, so its not as simple as just run a drain along it