I've rented with Avis in Scotland the last five or six times over. Never had a problem. I use my Visa card to cover the insurance in Scotland. They paid for a scratched alloy (wheel cover) on my last trip.
Ireland is a whole other situation. Visa/MasterCard will not cover you in the Republic. You have to purchase your own. And it is expensive. It will most likely double the cost of your rental. For a two week period, you should probably pay about $260.00 plus tax for a four door compact with manual transmission, but they also tax the insurance.
See if you can find an AWD so you can get a discount on your rental, like AAA, Entertainment, AARP, etc.
You'll enjoy driving in both countries!