What happened to polygamous Mormon families after the leadership of the Church of Jesus Christ of Latter-Day Saints disavowed the practice in 1890? Did families just split up, or did any of them continue to practice polygamy in secret?

This is not a super easy question to answer because there aren't a lot of statistics on mormon families after the first manifesto disavowing the practice of polygamy. On top of that, the records don't usually differentiate between monogamous and polygamous marriages.

There are a few references about what happened though. The church stated that they did not see the manifesto as an excuse for men to abandon their families and made it pretty clear that their temple marriages still counted and that they needed to continue to support their other spouses. [Abraham H. Cannon diary, Oct. 7, 1890, Nov. 12, 1891.]

Many families seperated/divorced on their own naturally (my guess is that they weren't happy and only stayed together out of religious duty). But others continued continued to support their other spouses but stopped cohabiting with them. [Embry, Mormon Polygamous Families, 13–14; Francis M. Lyman journal, Dec. 15, 1893, Church History Library; Utah Stake High Council minutes, Aug. 5, 1892, Church History Library, Salt Lake City.]

Then you have the families who continued cohabiting and actually continued to live the same as before the manifesto and actually continued to produce offspring into the 20th century. [Kenneth L. Cannon II, “Beyond the Manifesto: Polygamous Cohabitation among LDS General Authorities after 1890,” Utah Historical Quarterly 46, no. 1 (Winter 1978): 24–36.]

The third group is what I think you were probably most interested in. What it came down to is that the church disavowed the practice of polygamy to protect itself from having it's property taken by the government for not complying with the law. The manifesto was a public cooperation which gave them that protection. The church didn't disavow the practice because they wanted to but as a means of survival. The church basically let those families be and the U.S. government either didn't have the resources and infrastructure in the western United States or didn't care enough to check every family and a confirm the we're not cohabiting. So, ultimately it's a combination of the LDS church accomplishing their goal of protecting their assets and the organizational difficulties the U.S. gov wasn't willing to work through.

Even after the first manifesto the church performed polygamous weddings in Mexico. One of the men in my family history was actually called to take on more wives post first manifesto. His first wife left him because of this and he lived out the rest of his days in Mexico.

P.S. I tried to get references for everything but I don't have them all on hand currently. I'll try to add more a bit later but there are some for you to mull over.