awk -v n=3 '/<Car>/ && !--n {getline; print; exit}'
Or:
awk '/<Car>/ && ++n == 3 {getline; print; exit}'
To pass the search pattern as a variable:
var='<car>'
PATTERN="$var" awk -v n=3 '
$0 ~ ENVIRON["PATTERN"] && ++n == 3 {getline; print; exit}'
Here using ENVIRON instead of -v as -v expands backslash-escape sequences and backslashes are often found in regular expressions (so would need to be doubled with -v).
GNU awk 4.2 or above lets you assign variables as strong typed regexps. As long as its POSIX mode is not enabled (for instance via the $POSIXLY_CORRECT environment variable, you can do:
# GNU awk 4.2 or above only, when not in POSIX mode
gawk -v n=3 -v pattern="@/$var/" '
$0 ~ pattern && ++n == 3 {getline; print; exit}'
sed,awk, or evengrep, it's advisable to make use of a XML parser.