1917 can. 1262 §1 (which has no equivalent in the 1983 Novus Ordo Code) says:

[Peters's transl.:] It is desirable that, consistent with ancient discipline, women be separated from men in church.
[🇻🇦:] Optandum ut, congruenter antiquae disciplinae, mulieres in ecclesia separatae sint a viris.

A Commentary on the New [1917] Code of Canon Law vol. 6 pp. 204-5 (PDF pp. 2729-30):

§ 1. Conformable to ancient discipline, it is desirable that the women should be separated from the men in church. The very division of the ancient basilica singled out the vestibule for the penitents; the catechumens were usually admitted to the rear of the nave; the faithful occupied the side aisles, the men on the right [Epistle] side of the entrance, the women on the left [Gospel side]. Those who were held in special honor by the congregation, as widows and virgins, and those who, on account of age or social position, were entitled to peculiar regard, had their place in the forward end of the aisles or in the transept. The different orders of the clergy were in turn distinguished, the bishop had his seat in the middle of the apsidal circle, while the presbyters were seated on either side of him, but at a lower level, the deacons stood near the altar and the inferior clergy had their place with the choir in the nave.⁶⁵ In this country it will, we fear, be difficult to carry out this “desire” of the Church, on account of our custom of family pews.

No. The only place I saw that was Amish and conservative Mennonites.

It's Catholic, and older than the Amish and Mennonites. Did you notice it said, "ancient"?

repeat

In some third world novus ordo masses you can still find this. Women and children on one side, men on the other, sitting on floors sometimes. I think woman may veil as well. You’re probably more likely to see communion on the tongue and what not too.

The only place you see it in western countries these days is during traditional Confirmations where men and women are separated.

No, families need not all sit together.  Younger male children who still clung to their mothers could sit on the women's side.

That type of division led to where Our Lord separated from Our Lady and St. Joseph at the Temple.

Due to fear of robbers, people travelled in groups, and the men stayed separate from the women.  They had gone down for Our Lord's coming of age, as it were, and younger boys travelled with the women while those of age with the men.  It was also when the young men were expected to learn their father's business and to begin working with them.

On the way back, Our Lady believed that He had gone with the men, while St. Joseph thought that He has stayed with the women, out of habit, since that was how they had gone down there.  It was about three days' journey, so that shows how little communication took place between the men's group and the women's.

That is why Our Lord responded that He was doing His Father's business, since He had come of age, meaning the work of His Father and not His foster-father St. Joseph.

Another point here is that people tend to think of Our Lady as questioning Him and even scolding Him, but that couldn't be farther from the truth.  She asked Him to explain it for their understanding, knowing perfectly well not to question the wisdom of His reasons.  That is why the Gospel says that she kept these things in her heart, i.e., once He explained the meaning of His actions, she would meditate upon the mystery He had unfolded to her.

In any case, people can figure it out.  There's no reason families all have to be together.  In many chapels, some men are singing with the choir or serving in the sanctuary, so they somehow figure it out.  Older girls can help out with the younger children.  Excessively troublesome younger children can be left at home, and some women can help other women, including extended family, where sisters, mothers, grandmothers will all help out.  I see plenty of that going on already, and there's no insurmountable situation.  In extreme cases, the father could step out to the vestibule as needed.  Usually when the father's assistance is required it involves taking one of the children out anyway.

Biggest reason is that women in particular, in this country, have some emotional attachment (not practical reason) for wanting to sit together, but that too derives from the modern notion of the nuclear family, an innovation unknown in nearly all cultures until the modern times.  With extended family, often living together, the women never felt "alone" or isolated or abandoned.  Women have this need for social support that they used to get from other women in the extended family but now believe they require their husbands for.  There are so many reasons this is very bad and harmful.  So many marriages break down because wives can't "connect" with their husbands in ways females need to connect ... but they never needed to before since they always had that connection with other females in their extended family.  This results also in the effeminization of men, since women increasingly expect them to fill various feminine roles that would otherwise be fulfilled by other women.  I could go on for hours about how the nuclear family has destroyed both family and society.  You'd have fewer feminist wives, since older women would guide the younger.  You wouldn't have women wearing pants and demanding men to fulfill various feminine needs, serving as Mr. Mom's, changing diapers, with men's restrooms even in Trad chapels equipped with changing tables, etc.

I go to a western third world country Sedevacantist mass. The fathers sit with the boys on one side, and the mothers with the girls on the other. The exception is small children, but the wives and husbands are always apart. No problem at all, and I suspect that our women folk are even more emotional than American women.

Do the parishioners do this willingly or does the priest demand it?  My guess is, the priest demands it.