The phenomenon known as heteropaternal superfecundation works as follows:
First, a fertile woman's ovum divides prior to fertilization, just the same as it would in the case of fraternal twins. Then, the woman copulates with two men in close succession. Both of the ova are fertilized by sperm cells from different men. This, as mentioned above, is known as heteropaternal superfecundation. The result is a pair of fraternal twins who are half-siblings.
The other phenomenon is called tetragametic chimerism.
Chimerism is a condition of a person (or any animal) who has two or more different populations of genetically distinct cells originating from different zygotes. Chimerism occurs through the fertilization of two ova by two sperm, followed by the fusion of the zygotes and the development of an organism with intermingled cell lines. In fraternal twins, this happens by means of blood-vessel anastomoses. A chimera formed from the fusion of two zygotes of differing sexes can, in some cases, develop into a true (fertile) hermaphrodite.
The third phenomenon which needs no explanation is the male-to-female sex change.

So without further exposition, here is the process involved in half-motherhood.

  1. Your mother is fertile with two ova loaded in the chamber ready to be primed.
  2. She has unprotected sex with two or more men, perhaps even hosting a "gang bang" party event.
  3. Both ova are fertilized by different men.
  4. The zygotes fuse with one another forming a tetragametic chimera. For the sake of argument let's say exactly one gamete had a Y chromosome so that you can be a hot sexy hermy with big bouncy tits and a huge cock mmm yeah.
  5. You are born. You have a mother and two half-fathers.
  6. One or both of your half-fathers undergoes a sex change.
  7. While your birth mother is your full mother, your other parents are truly and literally half-parents, and if they are now female, it is only correct to call them your half-mothers.