You can enable and configure the remote management service with the kickstart
command. It's not in the usual PATH, so you need to specify its full path:
/System/Library/CoreServices/RemoteManagement/ARDAgent.app/Contents/Resources/kickstart
Its option format is a little cryptic, but with some experimentation you should be able to get the effect you want (see Apple's KB #HT2370 and SS64.com's "man page").
Also, it must run as root, so from AppleScript, use do shell script with administrator privileges
. I think you'll need something close to this:
do shell script "/System/Library/CoreServices/RemoteManagement/ARDAgent.app/Contents/Resources/kickstart -activate -configure -access -on -restart -agent -privs -all" with administrator privileges