I'm so sorry this is all causing you so much stress
I agree I'd ask to go to the next scan - I don't think the weeks are printed on scan pictures, but estimated due dates (and therefore how far along she is) will be noted at the scan.
The last period doesn't mean much as some women do have very irregular cycles or months without periods, but if that is the case with her the chance of her prediction whenshemight ovulate, collecting sperm from a condom and successfully inseminating herself at the right time is incredibly unlikely. When you're actually trying to conceive you start to realise that it's not easy, and that many months of having sex every day at exactly the right time often isn't enough - so either she's lying to you or you've been very, very unlucky. If I had lots of money I'd be willing to bet most of it on the former.