Can't unweb from an item I'm holding onto when I quick-create a web.

[CorvidWithAGun]

Whenever I'm swinging/dragging something and then right click on something else to fast create a web, I can't let of of previous item without resetting my spider.

[Darkness Vortex]

Yes, if you are holding something with your web, right clicking will attach it to you so that you don't have to hold down the click for a prolonged time. Then you are free to create new webs without dropping your item. When you are done carrying the attached item, target that web and delete it.