Here there be monsters
The biggest problem with your scenario as presented is that the complementary genes in the female do not go into the "secondary oocyte" but into the "first polar body" ("2" below).
The first polar body remains in the perivitelline space beside the oocyte, but it is a tiny thing, generally considered too small to potentially make a zygote. It is emitted as a diploid during the first division of meiosis, and divides again afterward. I think the one below has already divided.
Now, because it's impossible, we should naturally expect to find such a case, and I will not disappoint: Bieber, 1981. In that case the polar body had not divided yet, and the resulting twin, within the chorion, was a triploid and severely deformed "acardiac monster". A 2015 review mentions polar body twinning without describing the possibility of diploids, so I'll assume this hasn't actually been demonstrated. I know the first polar body is a bit half-hearted about its division.
It should be relatively straightforward to obtain immature sperm while they are still linked by cytoplasmic bridges as illustrated above, do in vitro sperm maturation to obtain complementary sperm, and attempt some sort of fertilization of egg and a daughter of the first polar body. The resulting twins would share a chorion but monochorionic and diamniotic. Such a procedure would still be very likely to produce a malformed embryo due to the development of a very tiny zygote. I was concerned about epigenetic differences, but after a helpful comment, I did find a reference that the methylome is similar to that of the secondary oocyte, and a paper reporting that it is possible to transfer polar body nuclei to oocytes with 42% viability. Given remaining uncertainty and a lack of apparent medical necessity, it might still be more advisable to stick to routine human cloning with germline genetic modification. :)