We present new proper-motion measurements of optically emitting oxygen-rich knots of supernova remnant 1E 0102.2-7219 (E0102), which are used to estimate the remnant's center of expansion and age. Four epochs of high-resolution Hubble Space Telescope images spanning 19 yr were retrieved and analyzed. We found a robust center of expansion of alpha = 1(h)04(m)02.48 and delta = -72 degrees 01 ' 53.'' 92 (J2000) with 1 sigma uncertainty of 1.'' 77 using 45 knots from images obtained with the Advanced Camera for Surveys using the F475W filter in 2003 and 2013 having the highest signal-to-noise ratio. We also estimate an upper limit explosion age of 1738 +/- 175 yr by selecting the knots with the highest proper motions and these knots are assumed to be the least decelerated. We find evidence of an asymmetry in the proper motions of the knots as a function of position angle. We conclude that these asymmetries were most likely caused by interaction between E0102's original supernova blast wave and an inhomogeneous surrounding environment, as opposed to intrinsic explosion asymmetry. The observed nonhomologous expansion suggests that the use of a free expansion model inaccurately offsets the center of expansion and leads to an overestimated explosion age. We discuss our findings as they compare to previous age and center of expansion estimates of E0102, as well as their relevance to a recently identified candidate central compact object.