Have you had any trouble with the HOA trying to shut you down? 

Depending on the type of home, you may have HOA or condo fees as well.

My question is how is that going to play out with the HOA, would they care?

If the property is a condo or townhouse, review the HOA rules and ask to see the HOA's financial statements.

I've put several of my rental addresses (that are not within a restrictive HOA) in to see what is for rent on the site nearby and to get an idea of the rates being charged.

Besides the obvious of HOAs (just as an aside, don't shop based on the HOA fee), their fees and management, you have some danger zones down the line as well.

How to go about the current hoa, building plans, current homes on site, (that are being rented out).

. $1950(rental income) -$1250 mortgage-Insurance-HOA fees (if there are any)-Vacancy-Repairs-Home Warranty Company (if applicable)-PM company fees (if applicable) -Any utilities paid by you (if applicable)-TaxesECT. 

This will greatly cut into cash flow (assuming you have any).If you are going to STR out your places make sure you have the proper insurance, collecting taxes, permits, not against any HOA rules ect... to do so.

Insurance, HOA, Property taxes?