If you're wanting to send the data from your weather station to both Cumulus & WD then you'll need something like VirtualVP
. If you don't then only one of the programs will be able to interrogate the WS for the data or you'll get conflicts as they both try at the same time.
Unfortunately VirtualVP will only work if you have a Davis VP or VP2.
Once you've got this sorted out then there's no reason you can't run your website using data & images from both programs.
Edit: I see you have VP so you'll be OK with VirtualVP.