The parts in bold I have added. Does that work, do I have gaping flaws in my explanation, is it cool, or should I just try to think of a better idea?
You asked I suppose.

Her mother was, during the last war, 'called' to become a Substitute Shinigami to .
No real problem here. Maybe expand on it later? Would be nice to see some backstory of the previous war through a mortals eyes.

She survived, obviously, got married late in life, and was already (mid 40s) by the time she had Maiku. (That explains why Maiku is an only child.)
Not that this part matters much but the incidency of twins doubles when a woman has children over the age of 35. Like I said, it doesn't matter what so ever. Fun fact brought on by how it explains why she's an only child.

Maiku's father harbored a grudge against the Soul Society, for various reasons.
What reasons? It didn't stop him from marrying a woman who worked for them. Obviously he has to have found out at some point judging on later information.

One day, while they were still in Japan, Maiku's mother was attacked by a hollow. Unfortunately, the regular Soul Reapers arrived just a little too late. After defeating the Hollow, Maiku's mother seemed perfectly fine, but the Hollow had some ability to slowly infect its victim and slowly turn them into a Hollow.
They didn't check on her? She had depowered enough that a war veteran had an issue with a regular hollow but they didn't check her wounds or anything? Did they take her powers away after the War? If so, they left a defenseless woman after a fight with a Hollow without checking on her.

Maiku's father noticed this, but kept it hidden from the Soul Society.
How did he notice it when the Shinigami didn't? This part is really really important. How did a mortal man notice something that a Shinigami wouldn't notice?

When it became really apparent that something was wrong with her, he took his wife and his daughter to Latin America, where she 'died' and slowly became a Hollow. He managed to keep this all a secret from his daughter, explaining that it was just an uncurable sickness.
Why Latin America? Why didn't he go to Soul Society to maybe heal her? If there wasn't anything they could do they could have at lease Konso'd her and she'd have died and gone to Soul Society.

Just before she became a Hollow, she went to Hueco Mundo because she knew that she would attack her family first thing.
Why didn't -SHE- go to the Shinigami. If the answer to the above is "Dad doesn't like Soul Society" why didn't the Mother go? Same about the above. Even if she was going to die, she'd have been cleansed and gone to Soul Society. A much better fate than becoming a Hollow and she'd have known that.

Maiku and her father immediately went back to Japan.
You've covered this as "Secret job" sort of thing so...I guess that covers it but it seems rather...sudden.

When Shinigami came to her father to find out what happened (they suspected that she became a hollow) to the old Substitute Shinigami, he told them that he personally killed her after she hollified. They seemed to believe him.
So wait. They didn't know she was turning into a Hollow. Then she died. Which is something humans have a nasty habit of doing so they go check on her family because they think she turned into a Hollow because...magic? Then the father lies about killing her when she did turn into a Hollow because...why? Normal human mortal kills a hollow but couldn't help protect his wife? Did they actually believe him or did they think "Hey wait a minute. This makes utterly no sense."

As time went on, Maiku's father (irrationally) blamed the Soul Society for Maiku's mother's death.
So far it seems like it's on the Father, Mother -and- Soul Society for her dying. The Shinigami for not checking on her after the fight. The Dad for not saying "Hey, I know you're turning into a Hollow because magic. Go to the Shinigami." and the Mother because "I'm turning into a Hollow. Guess I'll just die and turn into a Hollow. Ho hum."

I hate to use the word but...the idiot ball has been passed around freely here.

He found a human-based organization that does research on hollows.
We only see two mentions of mortals who have dedicated themselves to Hollows in the manga. Quincy and Xcution. The latter is just kind of a throw away plot and marks the last decline in the manga but the Quincy are good precedent. However, throwing this information out has a lot more consequences and impacts on the wider storyline and if it is introduced...it needs to be expanded on storywise. Otherwise it's a massive plot hole.

(I thought of this because it helps explain lots of her backstory - it explains how her mother died,
It does? You mean the whole back story or just the Anti-Hollow Organization. You added it in parentheses at the very end of the above so it's hard to tell what you mean. If it's the former than...ya. It explains how she died in a way. It seems to this outside observer that if even one party had cared a little more things would have turned out differently however.


it explains why her father is doing a Top Secret Hollow Research
It doesn't actually. It explains, kind of, that there is an Ant-Hollow Organization running around. Doesn't explain how he got involved what so ever or how he is even qualified other than "My wife was a Substitute Shinigami and I've seen Hollows."

and it explains how Maiku develops Hollow-type Spirit powers.
Suppose it does. Would explain why she's spiritually empowered of any sort just by her mother having been a Substitute Shinigami.

It also gives a good early-on conflict in the Mortal Realm, with Maiku's Hollified Mother coming and attacking Maiku and anyone else nearby.)
I have no stock in the mortal world but it would yes.




So....I suppose in sum up. It really really feels unfinished in a lot of ways. There are a lot of plot holes and other parts of the story that kinda connect strangely. I'm sure it makes more sense in your head but we can't hop in there. Hopefully all this has helped a little to point out some of the problems.