Our triad isn't exactly long-standing, but I think we've come up against some of the issues you're experiencing. We ALL worry occasionally that the other two might go off and be a happy couple together. Which is dumb, it's not going to happen. We all realise it's dumb, but we still worry.
The best thing we've found for working on that is to bring it up whenever it strikes. This does require a certain amount of bravery, but it means that we're all able to give reassurance when it's needed.
I understand how she's having insecurities when you two have been together for so long. My gf and bf have been together for 11 years, and married for 8, and naturally they have a comfortable way of being together. That's not something that will change (I hope! It's a great vibe to have) but it might become easier for her when your relationship as a three has settled in the same way. A year is still (relatively) new, and it's a lot to adjust to for all of you.
It sounds like you're doing everything I'd advise - keep talking it out, keep reassuring her, and I don't really know what else to recommend. I'd hope this will fade with time, when it becomes obvious that you're not going to leave her. I'd hope