This is an rather complicated question.
1. You cannot remove a product like vodka and carbonated water from the DSP premises in bulk (1.80).
2. You can do so in cans (see another post I made today on the issue of cans).
3. Removed in a can, it is not vodka, because it is not 80 proof (5.22). It would be a specialty item (5.35).
4. A fanciful name is required. So is a statement of composition unless it is a recognized cocktail, which I doubt.
5. If you remove the vodka (80 proof or more) , to the tasting room, in one gallon containers, and dump it into a barrel, then mix it with seltzer, and you have rectified it.
6. But premixing cocktails is deemed exempt rectification if you comply with some rules that TTB published years ago about premixing batches of margaritas. As I recall, that ruling is not easily found. My recollection is that it must be mixed for immediate consumption, which is defined to be consumption within 24 hours. I can’t give the site right now because do not know it.
7. Similarly, the premixing doesn’t violate rules that prohibit a retail form serving from other than the original container in which bottled.
8. Again, I would have to search for that ruling. It is going to say whether the premixing is possible.
9. But remember, if it is possible to premix, in a bulk container, under the rules I’ve not cited, you must do so on the tavern on the brewery premises (yes, you can serve spirits and wine there, as I assume you know) using spirits that were in containers of one gallon or less, that were properly labeled when you withdrew them from the DSP on tax determination an d received them on the tavern premises.
10. Neutral spirits are spirits distilled at more than 190 from any substance. It does not matter that the distilling material was derived from beer or wine. In whatever dilustions, it is a spirit and subject to spirits standards of identity (unless it is a mixture that is more than 50% wine on a proof gallon basis (5.11), which seems not to be what you have in mind at at.