Designing from small template for large canopy causing issues

I'm using a template given to me by a manufacturer of canopies, sidewalls, and table cloths. We had the tablecloth produced and the vector lines were fuzzy.  

Before sending in another file for the canopy, I wanted to get some advice on how to clean up the lines. Do I need to enlarge the template? 

The background is dark blue, the logo is white in vector. Would adding another darker line on the outside of the logo help with a cleaner output on cloth. Knowing it is going to enlarge to 20 feet, I know that keeping the line at a small enough point size conversion is best.

I've worked with screen printing on tshirts, and had not had this problem. But my first time larger than a 10 ft. banner using a small template.

Thank you in advance.