JMorgan,
use a while loop to continuously receive and check your data. In a loop one can create a shift register SR (right-click on the loops border). Initialise this SR from its left ide with an empty string. Inside the loop, read al availabel bytes at serial port and append it to what is in the SR. Match the result with 0x0d and, if found, send the substring before 0x0d to your subVI and the remainder to the right side of the SR. If nothing was found, send the substring before match to the right SR.
You should as well have a wait 100ms inside the loop.
Stop the loop when you're done.
HTH and Greetings from Germany!
--
Uwe