Bash – calling a command from script and maintain styling

Your quoting is wrong. When you write $CMD with no quotes, the value of $CMD is broken up into “words” at each whitespace sequence¹ (the words can contain any non-whitespace character including punctuation), and then each word undergoes globbing (i.e. wildcard expansion). Note that quotes in the value of CMD, in particular, are untouched: quotes have a meaning in the syntax of shell scripts but not in variable substitution. After this, the first word becomes the name of the command to execute, and subsequent words are the command's arguments.

In your example, assuming $KEYNAME is somekeyname and $HZID is somehzid, then the command and arguments are:

./dnscurl.pl
--keyname
$KEYNAME
--
-X
POST
-H
"Content-Type:
text/xml;
charset=UTF-8"
--upload-file
/tmp/file.xml
https://route53.amazonaws.com/2010-10-01/hostedzone/somehzid/rrset

Note that text/xml; appears as the first non-option argument; clearly the Perl script passes that argument down to curl. The -- in the argument list is unrelated to your problem.

There's no way to stuff a command line into a variable. A (simple) variable is the wrong tool for that: it contains a string, but a command line is a list of strings (the command, and its arguments). You can stuff a command name and its argument into an array variable:

CMD=(./dnscurl.pl --keyname "$KEYNAME"  --
     -X POST -H "Content-Type: text/xml; charset=UTF-8"
     --upload-file /tmp/file.xml
     "https://route53.amazonaws.com/2010-10-01/hostedzone/$HZID/rrset")
RESULT=$("${CMD[@]}")

The strange-looking syntax "${CMD[@]}" expands the array variable CMD to the list of words in the array. The double quotes prevent expansion of words inside the array, and [@] is needed for historical reasons to tell the shell that you want to expand an array.

Another way to remember a command line, or an arbitrary shell snippet, for later use, is a function.

cmd () {
    ./dnscurl.pl --keyname "$KEYNAME"  -- \
                 -X POST -H "Content-Type: text/xml; charset=UTF-8" \
                 --upload-file /tmp/file.xml \
                 "https://route53.amazonaws.com/2010-10-01/hostedzone/$HZID/rrset"
}
RESULT=$(cmd)

¹ _{More precisely, according to the value of IFS.}

Just for completeness, you don't need all those (") nor the final $(echo ...). Here's the simplified version of your assignments that produce the same effect:

STARTIME=$(date +"%T")
ENDTIME="$STARTIME today + 10 seconds"
CALL="date -d '$ENDTIME' +'%H:%M:%S'"

Note how you don't need to quote when doing var=$(...) but you do usually with var="many words":

a=$(echo 'a    b'); echo "$a" # result: a    b

Inside (") a (') has no special significance, and vice-versa, eg:

a="that's nice"; echo "$a" # result: that's nice
a='that "is nice'; echo "$a" # result: that "is nice