Learn English – Plural form of “brother-in-law” when a possessive case is involved

No. The rule is simple:

• For regular plurals ending in s, the possessive suffix is '.
• In all other cases, the suffix is 's.

Children is an irregular plural, not a regular one. Therefore, the suffix is 's, and the possessive form is children's. Your form *children's' is incorrect.

However, the other possessive forms are fine. Parents is a regular plural, so the possessive suffix is simply '. That means parents' is correct. And you correctly write children's later in the same sentence. (Was your earlier mistake a typo?)

In this answer, the * symbol means that the spelling is considered incorrect.

As noted in comments, it's generally (unofficially) discouraged to use "women" or "woman" as an adjective. It's preferred to use "female".

So, while these may be perfectly fine, they are not adjectival uses of "woman":

The woman pilots the plane.
At Airline X, women pilot all of the planes.
_{*Note that in these examples, "pilot" is a verb, not a noun.}

The preferred use would be:

Female pilots were well known as early as the 1960s.

As a note, none of these uses are "possessives". There's no show of ownership at all. It's just describing the type of pilot you're talking about.

This section options 1 and 4 both use the possessive but 2 and 3 do not:

1. Women's jobs
2. Women jobs
3. Woman jobs
4. Woman's jobs.

So, if your goal is to understand the possessive use, I'll ignore 2 and 3, which I don't think should ever be used, regardless of possession.

Version 1 is plural possessive. If that's what you're looking for, this is your choice. "Women" is plural and the "apostrophe s" makes it possessive.

Version 4 is singular possessive. "Woman" is singular and the "apostrophe s" makes it possessive.