As parents we worry about our children 24/7, we can't help it.
My DS is 13yo (going on 20 in his mind) and I worry about him constantly when he is out with his friends/staying at a friends house.
As parents we have to gradually get used to the idea that our children are growing up each and every day and will want to experience new things as they go along. We want them to spread their wings as they grow but it's difficult for us.
To be asking to take your niece overseas for a holiday, is from your perspective not unreasonable. What you have to understand though, is that even though you obviously adore your nieces, you don't have the same feelings as your sister.
I do not doubt that you love them with all of your heart, and neither does your sister. She obviously has every confidence in you as a carer, she trusts you, she knows you will always look after them. So much so that she is more than happy to have you play, what is obviously, a large part in their lives. She does trust you.
The issue about taking them overseas though, does not lie with anything to do with you, it's just something she, as a parent, is not ready for yet.
Give it a few years and I am sure you'll find things will change. She's a parent, there are no manuals for being a parent, it's something we muddle through and learn about as we go along. What you're asking is a big thing. To take her child out of the country. Whether it is quicker to get to somewhere in Europe than it is to Cornwall or Scotland, is irrelevant. It's the comfort of knowing your child is not in a foreign land without you.
Please understand this is nothing to do with your capabilities as an Aunty, you are doing a great job and it is obviously one that your sister greatly appreciates and is keen to encourage. She's just not ready for this yet.
Be kind, and others have said, start off smaller and in the UK. If you don't want to do that, then that's fine too. Wait a bit and see how things are in a few years.
My son has been on lots of holidays with my Mum, and he loves his Nan dearly and I trust her implicitly. However, she has never taken him overseas. I've never before felt comfortable with that. She is though taking him to New York for his 14th birthday. He's a bit older now and I'm feeling comfortable with this. I'll still be a bundle of nerves while he's away though, but I have reached the stage where I am ready for this
.