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.
If you now needed an alternate to this 'new destination', where would the required fuel come from? If you luck was out, and your alternate became unusable, are you suggesting you can now divert to this new alternate? And does it now require yet another alternate? And where would all that fuel required come from ....... and so on to absurdity.
Of course not - the reasoning is false, but even ATC can get it wrong:
I once held at Geneva for the weather to improve. It didn't, so I asked ATC for a clearance to Basle, my alternate. He asked me for my new alternate. I told him I didn't have one, but he insisted. I was holding at the VOR "St Prex" and could see the ground beneath me. There was a large flat green grass field below me, so I told him the grass field at my present position would be my new alternate - he accepted it!