You do NOT need an alternate to an alternate, and simple logic will show you why.
If you divert from your destination to your planned alternate you are diverting! You may now refer to your alternate as your new destination, but it is still in reality your alternate.
Diverting from destination to an alternate allows you to land with 30mins fuel at alternate. The sequence & route flown is approach to destination then divert to alternate. You would have arrived at destination with reserve fuel or more.
If the alternate is located before the planned destination, and for arrival fuel reasons you fly direct to that airfield, i.e. land short, then you have not diverted but changed the airfield to which you will make your first approach. You should arrive there with reserve fuel to a newly nominated alternate. i.e. when you make your first approach to land there would normally be an escape route called an alternate.
If you are suggesting that you could fly to your original alternate, without another alternate because it is your alternate, then by inference you could land with 30mins rule. Would you? I hope not.
If you arrive overhead your original destination and decide to continue direct to alternate that is a different scenario. You would have arrived over destination with planned reserves. Totally different.