When the engine is off, the brakes won't work, so the pedal being hard to push down when the engine is off is normal. It's a bit hairy being towed behind another car, having one hand on the handbrake and leaving it in a high gear, and lifting the clutch as a brake.
Make sure that the fluid reservoir cap is on tight
Check your brake pads to see if there's enough of them left.
There may be a pocket of air in the brake system, get it sorted quick sharp. The brakes need bleeding for sure.
If you get no gains from doing the above then you may have a faulty master cylinder or brake servo.