Can I run a command WITHIN another command?

You can try escaping the command like so

twidge update "$(date)"

Which will execute date and concatenate the output of the command into the twidge command.

According to the twidge help info

You can also omit the status, in which case a single line will be read from stdin and taken as your update. Example:

date | twidge update

Just pipe the command to twidge via stdin.

Yep, if I understand you properly, this will do it:

twidge update `date`

If twidge doesn't like it, try twidge update "$(date)", quotation marks to pass it in as one long string.