Sgr A*, the supermassive black hole (SMBH) at the center of our Milky Way Galaxy, is known to be a variable source of X-ray, near-infrared (NIR), and submillimeter (submm) radiation and therefore a prime candidate to study the electromagnetic radiation generated by mass accretion flow onto a black hole and/or a related jet. Disentangling the power source and emission mechanisms of this variability is a central challenge to our understanding of accretion flows around SMBHs. Simultaneous multiwavelength observations of the flux variations and their time correlations can play an important role in obtaining a better understanding of possible emission mechanisms and their origin. This paper presents observations of two flares that both apparently violate the previously established patterns in the relative timing of submm/NIR/X-ray flares from Sgr A*. One of these events provides the first evidence of coeval structure between NIR and submm flux increases, while the second event is the first example of the sequence of submm/X-ray/NIR flux increases all occurring within ~1 hr. Each of these two events appears to upend assumptions that have been the basis of some analytic models of flaring in Sgr A*. However, it cannot be ruled out that these events, even though unusual, were just coincidental. These observations demonstrate that we do not fully understand the origin of the multiwavelength variability of Sgr A*, and show that there is a continued and important need for long-term, coordinated, and precise multiwavelength observations of Sgr A* to characterize the full range of variability behavior.