Pride of Barbados, Caesalpinia pulcherrima is a member of the pea family (Fabaceae). It is a non-native plant in Texas, although it is frequently planted as an ornamental plant in the San Antonio, Texas area. This link to plantanswers.com indicates it to be a native of the West Indies and tropical America. It has escaped cultivation in South Texas, the Gulf Coast, and South Florida, and can be considered invasive in parts of its distribution.
Our focus at the Ladybird Johnson Wildflower Center is to increase the sustainable use and conservation of native wildflowers, plants and landscapes. Since the plant is a non-native, it is not found in our NPIN Database. In the material that I have read, there seems to be no problem with transplanting young seedlings as long as you get as much of the root as possible and place them in good potting soil.