Hi, if she is pregnant now with a viable pregnancy, it would not be your child. The GA count begins on the first day of the last period the woman had, or on the computed first day if her cycles are irregular, not on the assumed date of conception. If the sex on October 26 had produced a pregnancy, her GA count would have begun on October 12, making her something like 11 weeks pregnant on December 23.
There is a flaky Internet story floating around that sometimes women can hold onto an embryo and not let it begin to develop for a while. I have not seen ANY scientific evidence saying this happens. Failing that, the only way what the ultrasound saw would have been from you is if it is a nonviable pregnancy and has not passed yet.
I agree with Annie.
The ultrasound on Dec. 23 that indicated a sac at 4.3 weeks gestation but nothing but the sac was seen - would indicate she became pregnant around Dec. 9th if it's a viable pregnancy. Two weeks later, which would be 6.3 weeks, you can expect to see a heartbeat but nothing at all was found in the sac from what I can tell.
I don't think this is a viable pregnancy, and if it is, it's certainly not yours - the timing is very far off.
If it's a failed pregnancy and she has somehow not miscarried the sac yet, it's possible it was your baby that never did begin to develop properly.
BTW - there's way too much information in your post that makes it difficult to wade through and find the pertinent information. Fights, 28 day reminders, trips with men, when she moves out, etc., are not helpful in determining whether you are the father of a viable embryo.
All that is needed are the dates of the transvaginal ultrasounds, what was found during those ultrasounds, and the date of your last unprotected sex.
I am also a little confused. What exactly is a 28-day alert, and if it came about "due to an argument," what was it supposed to do to solve the argument? If it were a notation that her period was due than, wouldn't the main thing be for her to have such an alert on her own calendar? Why would it be on your calendar?