  Vinyl cyanide (C$_2$H$_3$CN) is theorized to form in Titan's atmosphere via
high-altitude photochemistry and is of interest regarding the astrobiology of
cold planetary surfaces due to its predicted ability to form cell membrane-like
structures (azotosomes) in liquid methane. In this work, we follow up on the
initial spectroscopic detection of C$_2$H$_3$CN on Titan by Palmer et al.
(2017) with the detection of three new C$_2$H$_3$CN rotational emission lines
at submillimeter frequencies. These new, high-resolution detections have
allowed for the first spatial distribution mapping of C$_2$H$_3$CN on Titan. We
present simultaneous observations of C$_2$H$_5$CN, HC$_3$N, and CH$_3$CN
emission, and obtain the first (tentative) detection of C$_3$H$_8$ (propane) at
radio wavelengths. We present disk-averaged vertical abundance profiles,
two-dimensional spatial maps, and latitudinal flux profiles for the observed
nitriles. Similarly to HC$_3$N and C$_2$H$_5$CN, which are theorized to be
short-lived in Titan's atmosphere, C$_2$H$_3$CN is most abundant over the
southern (winter) pole, whereas the longer-lived CH$_3$CN is more concentrated
in the north. This abundance pattern is consistent with the combined effects of
high-altitude photochemical production, poleward advection, and the subsequent
reversal of Titan's atmospheric circulation system following the recent
transition from northern to southern winter. We confirm that C$_2$H$_3$CN and
C$_2$H$_5$CN are most abundant at altitudes above 200 km. Using a 300 km step
model, the average abundance of C$_2$H$_3$CN is found to be $3.03\pm0.29$ ppb,
with a C$_2$H$_5$CN/C$_2$H$_3$CN abundance ratio of $2.43\pm0.26$. Our HC$_3$N
and CH$_3$CN spectra can be accurately modeled using abundance gradients above
the tropopause, with fractional scale-heights of $2.05\pm0.16$ and
$1.63\pm0.02$, respectively.
