Can you sue your own homeowners insurance if they don't repair your house properly after a water leak?

Your insurer paid the bill presented by your chosen contractor who made the repairs you requested. That was all they were required to do. So, you could probably sue, but you probably could not win.

If your repairs were performed substandard, your claim is against the contractor who did the shoddy work or your contractors insurer, not the insurance company who already paid the bill.

The insurer is not responsible for the quality of contractor an insured hires nor are they liable for the poor quality of that contractors work.

The insurer can not be made to pay twice for the same repairs. This is why it's important that you hire a reputable contractor and verify they are adequately licensed and insured (get a copy) before allowing any work to begin on your home.