Your issue is not the bike as your road bike tyres will hardly stick to the road at that speed on a 90 deg bend. My only suggestion is to firstly make sure there are no cars around either direction, go wide early, brake gently as going out. Release the brake but keep your fingers on the lever, and then cut back across the corner. I use Vittoria rubino pro tyres which stick fantastically for my style . Monitor your speed and force on your tyres and pedal out.