In modern information security, Vignere is broken and therefore irrelevant. The only secure option is to use good ciphers, so this question precludes information security given the current state of the art.
Cryptography probably won't be interested, as these algorithms in general are completely broken. They are of passing historical interest at best. It would be like asking a modern doctors about the balance of humors.
I believe Worldbuilding.SE is the best forum, as there seem to be a lot of technically-minded folks there who are interested in niche and fantastic scenarios. That said, crypto is an uncommon area of interest.
I'm have only been on Worldbuilding.SE once or twice, so I could be wrong. Regardless of which forum is ultimately correct, my response would be:
If you use a very long key sequentially---and replace it before you run through it completely---then it is effectively a one-time pad and is very secure. (Provided the new key/pad is distributed securely.)
Each message must indicate where on the pad to begin, otherwise a missing or incomplete message would render subsequent messages indecipherable. Or perhaps you could neglect this issue and let it become a plot point.
For the sake of consistency, your characters should understand that their total biweekly communication cannot exceed the key length. This would add some terseness to the messages and potentially some plot tension if one character needs to communicate as his pad is running out.
If this "due diligence" mitigation of Vignere brokenness needs to be overcome, you have options. The adversary can simply start intercepting and making copies of their pads. Alternatively, the one-time pad may not be truly random, and the adversary could determine how it is created.