front end shakes when towing and applying brakes

Hello, it is likely due to excessive brake rotor runout especially when the brake fluid and brake friction materials are exceptionally hot. Certainly, get the first hand opinion of a local technician near you. If the brake rotors are the source of vibration, they are covered under warranty for resurfacing for the first 3 years / 36,000 miles -- so seeing your dealer may not be a bad idea.