Mudguard/fender width advice
3mm is definitely not enough, especially with plastic fenders! 

A good rule of them is your fenders should be at least 10mm wider than your tires. I run 42mm tires on one bike and it has 58mm fenders. On my other bike I run 32mm tires and 45mm fenders. You also want at least 12mm between the inside of the fender and the tire. Ideally, you should have 20mm between the tire and point on the frame the fender bolts to (to account for fender thickness, protruding bolt heads and mounting hardware). 

Keep in mind poorly fitted fenders can be a safety issue. If an object gets kicked up into the fender it can cause a crash. 

Some good articles on fenders: https://janheine.wordpress.com/category/components/fenders/ (Jan probably knows more about fenders than anyone in the cycling biz!)