I have read your question completely and i will try to help you with some technical inputs.
A pregnancy test can be positive after implantation of the fetus.The blood pregnancy test is usually positive within 3-4 days after implantation.This is called as quantitative beta hcg test.
Implantation means when the fertilized egg implants into the endometrium.
As after implantation the fetus is connected with blood stream of the mother so the the pregnancy hormone is released in the mother.
So basically it is possible to have a positive beta hcg test about 9-10 days after fertilization/conception/intercourse.
So if you have intercourse around 12th April it is possible to have a positive beta hcg on 23rd April.
Also the level of hcg hormone in twin pregnancy is higher.
Probably the further details are quite non technical and difficult to comment on exactly what is happening.
So if further reports of ultrasound etc are availaible it will be great.