I had my tubes clipped after difficult child 3. Then a few years later I got a letter telling me that in the month or so that I was getting 'clipped', they had a problem with their clip thingie and a lot of failures have resulted. I was supposed to go back to the hospital to have tests to see if the clips were doing their job with me.
I was really upset, the test they wanted would have been nasty so I refused. My GP looked at some recent X-rays and said that they showed the clips were in the right place; if they had fallen off the clips would be down near the lower part of my pelvis, and they weren't.
Sometimes things fail. And I HAVE heard of cases where a woman's tubes were tied but she already had an embryo working its way down the intact part of the tube to her uterus, to implant. The pregnancy may have a higher likelihood of miscarrying in the few weeks after surgery, but after that it is as stable as any other pregnancy. Only if they took your ovaries out, would you miscarry automatically without medical intervention.
There is also a faint chance you have become pregnant since the tubal ligation, but from the dates you mention it sounds like you were already pregnant (a week or two, maybe) when you had the ligation.
I also remember a woman in New Zealand who had a hysterectomy - they removed the entire uterus, but left the ovaries, because it makes menopause easier to deal with - and at the time of surgery, she had a fertilized egg in her tubes. The egg fell out into the abdominal vault and implanted in the rich blood supply on the outside of her intestine. It took them a while to realise she was pregnant, but hormonally the ovaries kept the pregnancy viable until the uterus took over at 14 weeks. She was very much at risk and spent most of the second half of her pregnancy in hospital being monitored, but she had the baby OK. She had to have a caesarean, of course, and they also had to take some of her intestine because the placenta was not going to come away without it, but eventually she was fine. The baby was perfect.
I think it was something unusual like that used for the plot in "Junior" where Arnold Schwarzenegger gets pregnant.
Basically - if you ARE pregnant, there's no reason for there to be more of a problem, but get to your doctor ASAP if you get another positive on the home kit. The time delay could have given you a false positive, too.
husband's cat, when he was a kid, had a tubal ligation soon after weaning a litter of kittens. But it was too late - she was already pregnant, although that surprise one was her last pregnancy.
Marg