visits in the country during the renovation to check on workers and contractors and to show the house since I do not want to use an agency?
You could try to apply for a B-1 Business visitor category, or better yet, for a B-1/B-2 visa.
There is no special or specific visa category for what you are trying to undertake. If your country of nationality has an E-2 Treaty with the US, you can then see if you'll qualify for an E-2 Treaty Investor visa, since you purchased the house for rental. Difficult.
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