To answer your direct question first...
I agree with the mug assessment. Good idea to get rid of it. Truth be told, however, I preferred that plaque to the others. Having said that...
OK, so I'm going to go analytical on you. Your brewery name is Two Track Brewery. Your logo has nothing to do with "two tracks." You don't need a picture, but the purpose of a logo is to represent the feeling/purpose/direction of your brand. So my question to you is, what does a wooden plaque say about your brand or how does it tie into "two tracks?"
If the answer is "I don't know" or "I thought it would look cool" then perhaps you should think about what what you want your logo to say. You took the time to name your brewery so your logo should somehow relate to that and both should say something about your brand (why that's important to you, what you want people to think about when they hear/see your beer, etc). Believe it or not, people will form an impression on a product or company based on your logo - even when the logo is for somebody's hobby.
Sorry to dive so deep. My wife is a graphic designer and I've heard this conversation a million times with her and her clients.