I'm confused as to how having two Ethernet ports close to each other could lead to the cables becoming insecure. Once an Ethernet plug has been pushed into its socket, it should 'click' home in such a way that a couple of championship-winning tug-of-war teams couldn't pull the connection apart.
If you're forced to get a new router then (unless you need a model with the absolute maximum wi-fi range) ANY router with more than two Ethernet ports should meet your requirements (since you can use, for example ports 1 & 4, so that the cables won't some close to each other). I'm perfectly happy with my ZyXEL model:
http://www.cclonline.com/product/77596/AMG1202-T10A-GB01V1F/ADSL-Routers/ZyXEL-AMG1202-T10A-150Mbps-802-11n-Wireless-N-ADSL2-Router/NET0541