You haven't got it quite right yet. Not to worry. As I said, the whole thing is complicated and unless you work with it daily as I do, it is impossible to remember.
When the egg gets to meiosis II, there are only half the usual (diploid) number of chromosomes. However, which half of the chromosmes the eg ends up with is random. For each pair of the 23 pairs, it could have one of the chromosomes contributed by the father or one of the chromosomes contributed by the mother. Mix and match, as it were. With regard to sex chromosomes, the egg is always left with an X chromosome because females always have two X chromomses. Half the chromosomes (which half is random) go to the first polar body and they do not contribute to resulting embryo. Instead of having the diploid number of chromomses (two copies of each chromosome), the egg now contain one copy of each of the 23 chomosomes.
The sperm determines the sex of the resulting embryo as sperm carry eith an X chromomse (that it got from the mother) or a Y chromomse that it got from the father. XX = girl and XY = boy.
Each chromomes has two "sister" chromatids. After the sperm enters, but before the sperm and egg chromosomes are combined in the nucleus of the resulting embryo, the egg excrudes a second polar body containing half of the sister chromatids for each of the chromosmes. The sister chromatids contain vertually identicle copies of the DNA. They are not completely identical becasue of "crossing over which occurs at an earlier stage. The crossing over story is for another day. The result is that the egg now contains half the number of chromosomes (23 single chromomes instead 23 pairs) and half the number of sister chromatids (each chromosome split at the centromere to produce two single chromatids - half a chromosome). This completes the meiotic process for the egg.
So, in the end, there are two polar bodies, not three.
The sperm has completed the meiotic process before entering the egg, so it brings in half the number of chromosomes and half the number of chromatids. The chromatids from each parent then replicate before the first division so that each chromosome has two chomatids. After the replication, the result is the original diploid number of paired chromosomes (23 paired chromomses - half from the sperm, half from the egg) and, after replication of the DNA, each chromosome now has two sister chromatids. The haploid pronucleus from the sperm and the haploid pronucleus of the egg then migrate towards each other and fuse creating the diploid embryonic nucleus. Now the embryo has the correct amount of chromsomes (2n) and chomatids to begin dividing (1 cell to 2 cell, 2cell to 4 cell and so on).
The maximum hCG level is reached about 24 hours after the shot. So, when we test the hCG level about 12 hours after the shot, it is still rising. If its low, that means the time of the injection was later than it should have been, since it hasn't had time to rise appropriately. Consequently, the follicles haven't been exposed to enough hCG yet and that will delay maturation, which is completed around 36 hours after the hCG injection. Ovulation (if allowed, which its not in IVF) would occur around 39-42 hours after the hCG injection, when the eggs have had a sufficient time to undergo the final maturation.