Will an ultrasound scan date be accurate enough to determine who the father is if you have slept with 2 different men within a month?

No. The only way to be absolutely certain of who the father is, is a paternity test. Most people still choose the standard blood test. DNA testing is 99.9% conclusive, but is more costly. Ultrasound only indicates the growth and health of the fetus. A calculated guess can be made on the "age" but definitely not the paternity.