yes put the sound deadening inside the door probably the best solution. if you can have a new door frame, you can have wider rubber seal to seal the door too.
if you have time, take some time to reclaimation street to visit those shops selling those sound deadening. there is a "kin choi shockproof material" (http://www.kinchoi.com.hk/big5/aboutus.php) who has quite a lot of sound deadening material and some samples for demonstration. "hings rubber products" is also another shop selling some sound proofing materials but i found them not too professional.
if i have the money for a bigger home, sound deadening between rooms and ceiling and floor and of course the main door are needed.