If it were our job, we would talk the customer out of the smaller sign with the hours on it and go with just the restaurants name. The majority of successful restaurants don't advertise their hours on their main sign, and there is a reason for that. I'd even drop the "homestyle cooking" or at the very least really downplay that part. This way you have much more room for just the name and less additional content to confuse passers-by. A sign like this isn't a business card or a yellow page ad, it's a "here we are", "this is what we are called" statement, any other information about what type of restaurant this is should be portrayed by style and feel of the design. In other words, for a sign like this, less is more. Perhaps the hours would be better suited on or by the entrance. That is generally where people look for that information anyway. Just my 2 cents.
I think we have a winner!!
I agreed with your original post about removing the hours
But the fact of the matter in this case, from what I've gathered from Mr. Andrew is that the customer probably won't budge on revamping everything. Granted, my initial "The customer is always right" comment was slightly sarcastic, but I was just acknowledging that our man is bound by...dare I say it?...an ignorant customer. All of you guys are right, the client is not a designer and they don't see things in the same light as you hard working lads do, nor do they have the experience. They just know what they've had and what they want. Gino's dialogue suggestion was perfect, and you can educate the customer all you want, but at the end of the day, the money does all of the talking. I'm all for offering recommendations and providing solutions and educating the customer, but in circumstances such as this one, you just have to do your best to work within whatever restrictions you have.

for calling me a lad..... you little stinker.