Hi.
I work for a Bank, and work with debit cards on a near-daily basis. I thought I'd try to add my 2 cents.
Your debit cards on either the Visa or Mastercard network should work ANYWHERE Visa or MC credit cards are offered, but Kermit's right. They DO have some restrictions - a daily limit being a big one. I never considered the problem Kermit suggested - but he's (she) absolutely right. We have a $1000 daily limit on the cards issued at our Bank. And the resorts, in my personal experience, DO accumulate all your charges during your stay, and run them against your card at checkout. It will show up on your statement as being originated by (Resort Name) Front Desk. Maybe you could run by the front desk at your resort halfway through your stay and ask them to run a charge for the charges up to that point? Just a thought....
As far as rental cars. What a HEADACHE these have been for us at the Bank. First of all - the rental car agencies CAN process charges against your debit cards, but they have chosen not to, and there's a good reason why. The whole problem lies with the reservation process. When you reserve a car, and offer your card to hold it, an authroization is run against your card for the proposed amount. A "hold" is placed against your account for this amount. Now, if you're using a credit card, unless you're near your limit, this "hold" will probably be transparent to you. BUT!! If this "hold" is run against your debit card, those funds are not available to use on your debit card. This authorization can "stick" to your card for some times up to 10-14 days! Imagine the calls we've gotten from stranded customers who aren't able to pay their hotel bill to check out because of the authorization being held on their debit card!! And this authorization will often hold on "after" the charge has already cleared your checking account.
The "moral" of the story? Do NOT, EVER, use your debit card to "reserve" a rental car. For that matter, we've seen this happen with the reservation of hotel rooms, as well. (I even had a guy get stuck because of one that arose after a bar tab ran an authorization against his card!!)
But - you should "always" be able to make the final payment of your rental or hotel reservation with your debit card - just use a "credit" card to make the initial reservation. In my personal experience, they don't care if you use a different card when you check out/pay for the car than the one you used to hold it.
Hope this helps - wish I could communicate this to all my customers!