The dates are too close. Only way you're going to know for sure is with a paternity test once the baby is born.
I'm guessing that the 2nd doctor was right, because based on your LMP (first day of your last menstrual period) you would have been around 10wks along on May 18th...which puts your LIKELY dates of conception somewhere between march 29th to april 6th. it could honestly be either man's baby. you most LIKELY ovulated around april 2nd...and the ex-boyfriend's sperm would have been still alive and viable...but then, you added fresh sperm the very next day from a different man...so I think it's gonna be too close to call without a DNA paternity test after the baby is born. sorry!
sorry, you have confused me completely....