Personally, I would (generally speaking) choose a diff name. There are a billion names, I would find another one I love rather than have two babies with the same name. In my case, though, I love lots of diff names and i'm always changing my mind! However, in your case if there are absolutely no other names you love - then name her Isla. It's a gorgeous name and you already got their go-ahead. It sounds like they are ok with it, so why not?
Side note - In Elem school my best friend had the same name as me! We thought it was neat that we had the same name!! My point is - even if your daughters do grow up together, I doubt they will mind both being called Isla!