I kinda like this idea. So, with a mobile calling the Skype number, is it free? Or does the caller have a charge as well?
The sticking point in all of this is my sister's mobile. She can't use Skype but if she can call a Skype number for free I think that's the option for me!
This should work well for you. What you are paying for when you buy number from Skype is the ability for people who are not on Skype to be able to call you. If your sister has a call plan on her mobile or landline that includes calls anywhere in the US, it won't cost her anything. You can most likely even get a number that would be local to her, so even if she doesn't have the national call plan, it won't cost her anything.
Make sure you can use the Skype app on your mobile (your mobile needs to be able to connect to wifi.) If your phone does not do this, then you will either need to buy a skype phone or answer her calls on your computer.
If you already have a good/cheap way to call the States, then you only need buy the US Skype number. You don't buy the outgoing minutes from Skype, but you will only be able to receive calls. But if you don't have a good call plan, check out the offer from Skype. I pay £4.00 a month for unlimited calls to the US, good for calls to any US non-toll numbers, cell or landline.