Hi,
It's some kind if trafficlight. If you wish to go with $1 shop, you can have it "1 in red circle" and omit the two numbers, so do with 2 etc. I think we don't need a dollar sign inside the circle because the "Dollar" word is clearly spelled in the logo. These also could be a gimmick for your lighting on the shop sign, I'm sure it could attract audience.
The logo has been designed based on your below statement:
IMPORTANT NOTE: The shopping center we are in requires that our signs use "Channel Letters" so for purposes of signage, each dot and each letter must stand separately from the others. I’ve seen some great designs with dots or letter touching each other so I brought this up again with the landlord. He seems adamant the dots and letter stand separately.
Hope that helps.
Thanks,
FL.