Hello and sorry you're having problems.
Your Ipod is simply showing the 1st speaker as an available Blue Tooth connection since it's already connected with it once. The issue is that Blue Tooth only allows for connection of one speaker at a time- this is the same with all Blue Tooth devices. If you want to be able to connect to multiple speakers off of one device, then you would need a Wi-Fi speaker- such as the Sonos units, which give each speaker an IP address and can connect to as many speakers as you purchase.
BueTooth's limitation is connection to a single device at a time, that is the Blue Tooth protocol I'm afraid. Take this from someone with a line of Blue Tooth speakers. The availability of devices you can choose from is there- but only one can be streamed to at a time.
Alternatively, Wi Fi speakers offer much more diversity.
There is also another option if you want to continue to use the Bose speakers, and that is to purchase a Hi-Fly internet streaming box for each one (around $60 each) and connect to the speakers with an 1/8" AUX cord. This will assign each box a separate IP address and you can then stream music using the Hi-Fly APP.
Hi-Fly streaming box:
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