Within engineering education, informal, out-of-school making experiences and parent-child interactions within home environments are both considered as a promising context for the development of engineering discourse and practices. However, less is known about how parents support children's engagement in engineering learning, particularly when they are foregrounded with making that use materials and technologies that can introduce sources of uncertainty. To understand both the opportunities and uncertainties of centering making within parent--child engineering learning experiences, this study examines how parents' use of epistemic supports differ between engineering design tasks with technology and engineering design tasks without technology, and within the different phases in the engineering design process. The study further investigates how parents exhibit epistemic uncertainties differently between engineering design tasks. Building on the notion of guided participation to frame engineering learning and making as co-constructed through multiple situated interactions, this study demonstrates that: (a) parents are skilled knowledge practitioners for their children's engagement of engineering learning through the use of various epistemic supports; (b) the presence of technology in the engineering design tasks prompt different types of epistemic practices and engineering design phases; (c) opportunities and tensions co-emerge when parents experience epistemic uncertainty about STEM concepts or troubleshooting during engineering design tasks with technology. We discuss implications for the design of engineering design tasks within home environments that extend the use of parents' epistemic supports.