Open a business - lookup STEP programme. You can apply for permission to open and run a business in Ireland once you satisfy the requirement.
https://www.irishimmigration.ie/start-u ... whatisstep
Work for a business in Ireland - apply for an employment permit (usually critical skills or intra company transfer) as usual. The position being an executive or not is irrelevant.
Visit Ireland on business capacity - you get a standard business visa if you only occasionally visit Ireland for business purposes. Whether you have an Irish spouse or not is irrelevant. Having an Irish spouse will allow you to get a Stamp 4 (which allows you to do basically everything in Ireland), if and only if both you and your spouse intend to live in Ireland (i.e. more than 9 months in each year).
There is also a special IIP scheme which allows you to obtain a Stamp 4 but has no residence requirement whatsoever. The requirement isn't very high but places are quite limited.
http://www.inis.gov.ie/en/inis/pages/ne ... repreneurs