"Kawaika'a" (Kawayka) is a Keres word used by today's Hopis (and Lagunas) to refer to Laguna Pueblo and the Laguna people. However, in this case the name refers to a pueblo built on the rim of Antelope Mesa, beginning in the late 1300s and abandoned in the mid-1500s.
Small pieces of data I have found indicate the builders of Kawaika'a were likely part of a group migrating back and forth between Pottery Mound, Acoma and pueblos in the area of what is now Laguna.
In the pottery of Pottery Mound is a sequence indicating an influx of Acoma and Zuni potters between 1395 and 1415 with an influx of Hopi potters between 1405 and 1435. There were a few pieces of Jeddito black-on-yellow ware imported to Pottery Mound but most other Hopi-style pottery found was made at Pottery Mound. Some of the designs developed in those years survived the abandonment of Pottery Mound in the late 1400s by being transmitted to places like Awatovi and Kawaika'a. Shortly after their arrival on Antelope Mesa, those same designs made their way onto some of the pottery of Sikyátki.
The primary method of transmission back then seems to have been painted textiles. If so, we modern folks are missing a major part of the social record due to poor preservation of ancient textiles over the intervening hundreds of years. All we have now are the paintings of textiles that survive on some wall murals.
Many of the designs developed at Pottery Mound were perhaps more fully expressed at Awatovi than at either Kawaika'a or Pottery Mound. There's no way to be sure as Kawaika'a was abandoned in the late 1500s and many Kawaika'a potters moved to Sikyátki. Either way, the designs reproduced by Awatovi potters were produced in massive quantities for local consumption while those produced by Sikyátki potters were more refined and ended up spread across the region from the Pacific coast to the plains of Kansas.
Then in 1540 came Captain Pedro de Tovar, with a group of soldiers from Francisco Vasquez de Coronado's expedition. He'd been sent to see if the Hopis had any gold they could steal. He was met at the edge of Kawaika'a by warriors in battle formation. The fighting was over quickly, the people lost. Then the Spanish searched everywhere and, finding no gold to steal, they moved on to the next nearest village and repeated the process. Finally, they gave up on finding any gold and turned back to rejoin Coronado at Zuni.
The Hopi pueblos were not bothered by the Spanish again until the Franciscans arrived at Awatovi in 1629. Immediately after their arrival the quality of pottery across all Hopi mesas fell off, way off. The resulting sad product is now known as San Bernardo Polychrome (black-on-redware, named after the mission: San Bernardo de Aguatubi). By then, though, Kawaika'a had already been abandoned. Some of the people scattered to other Hopi villages, some probably made the journey back to the area of their ancestral homeland: Laguna and Acoma. Evidence has been found of an incoming migration at Laguna from around that time (Acoma is a living pueblo and nothing there has ever been excavated to know for sure).
Archaeologists found numerous wall murals in the underground kivas of Kawaika'a but none showed any of the imagery identified with Sikyátki style. The Kawaika'a murals were simpler, most were multi-colored designs of plants, flowers and geometrics. Some of those murals featured human figures in detailed ceremonial regalia with chiseled profiles emphasizing noses and chins. That is a style of decoration not seen elsewhere in the Hopi mesas but is found among examples of Jornada Mogollon rock art and among later Rio Grande art. The nearest Jornada Mogollon influence was most likely from Casa Malpais, which was abandoned around 1400. Some of those people may have migrated north to Kawaika'a along with some of the people from the Fourmile Ranch area.