As another possible solution, how about having the Meteobridge or the one connected PC software saves the data to an SQL database. Then a second program can use this SQL database as its source. If this works there is no reason that then there couldn't be a third or more weather programs that simultaneously access this SQL database. The only requirement is for these additional weather software programs to have the capability to access an SQL database as their source data. Does anyone know if the usual suspects can do this? You know WeeWx, Weather-Display, etc. If this is not possible then I'm sure it could be a change request that could be done to those software developers.
Which leads me to another thought. Just like you can have any number software programs open a jpg file or an mp4 file because there is a standard, there should be a standard for weather databases. Then easily several weather software programs could access each other's data. Or you could easily switch programs without cumbersome data export and importing. We need a weather database standard.