You'd be better off doing this with named hosts.
If you configure the vhosts to accept by name, then you could have something like this...
Listen 80
<VirtualHost *:80>
DocumentRoot "/var/www/alpha/public"
ServerName alpha.dev
# Other directives here
</VirtualHost>
<VirtualHost *:80>
DocumentRoot "/var/www/beta/public"
ServerName beta.dev
# Other directives here
</VirtualHost>
Then in your hosts file (on your local machine):
192.168.1.46 alpha.dev beta.dev
This will allow you to hit either site, by name, and point to the appropriate doc root.