404 is right but you don't need a plugin to solve the 301 problem.
The easiest way to do so is to make both domains point to the same virtual host (hosting company generally call this domain parking or domain aliases).
Once it's ready, reconfigure your wordpress to tell what's the new domain (
http://bestkidapps.net) so internal URL and redirects point to the right domain.
To solve the 301 redirect needed to avoid duplicated content (because both domain will display the same website), just use this simple rewrite rule (you can add it on top of your current .htaccess file (wordpress probably created one for you if you configured rewritten URLs):
RewriteEngine On
RewriteCond %{HTTP_HOST} !^bestkidapps\.net$ [NC]
RewriteRule (.*) http://bestkidapps.net/$1 [QSA,R=301,L]
Basically, it tells to 301 redirect every request to bestkidapps.net if the original request was not made on this domain.
HTH