The entry for Weeping Yucca (Yucca gloriosa var. tristis 'Variegata') says that it has two child plants.
One of them, Moundlily Yucca (Yucca gloriosa var. gloriosa 'TUSZYUC001'), is not a child plant of Y. gloriosa var. tristis 'Variegata'. It is a child plant of Moundlily Yucca (Yucca gloriosa var. gloriosa 'Variegata').

We run into that problem a lot in the Rose Database because so many roses have the same name. That's why some of the rose cultivar names include the year of introduction. The only way I can think of to correct it in this case is to give one of the Variegatas a slightly different name, such as Variegata 1 or Variegata Tristis. Neither of these changes will prevent the plant from being included in search results for "Variegata," but it will clear up the confusion in the parentage field.

Would changing the name slightly to get the right parent cultivar and then changing back work? Could putting a name in the also-sold-as field and then changing the name in the parentage field in the child plant to the name in the parent's ASA field work also?

No, the parentage link will go to the first plant that was added to the database with that cultivar name. The ASA field plays no part in the parentage link. Even a trade name won't create a link. It has to be the name in the cultivar field.

The system reboots every night and corrects anything that looks like an error at that time, so changing it and then changing it back wouldn't work either. It would just be "corrected" in the next reboot.

The fact that the links lead to the wrong plant can be easily fixed by changing "Sport of: Variegata" to "Sport of Yucca gloriosa var. gloriosa 'Variegata'" in the Parentage Field of Yucca gloriosa var. gloriosa 'TUSZYUC001'. Alternatively, simply removing the colon after "of" will break the link as well.

This will not result in linking to the "correct" plant, though, because the Child/Parent links only work with cultivar names. However, depending on how literal you want to be, sports probably shouldn't show in the Child Plants field anyway. A sport is a mutated clone of a plant, rather than its "child".