Homogenization has a fairly specific meaning in dairy. To keep the relatively large milk fat globules in cow's milk from coalescing, the milk is forced under some pressure through a very small aperture that atomizes the fat and keeps it in solution.
Although it seems like this might work with butter I doubt very much that this is a worthwhile solution (pun intended).
What you want, therefore, is to create an emulsion. Butter has some emulsifiers in it but I don't think it will be up to this task on its own.
The idea with any emulsion is to blend emulsifiers into the liquid and then slowly add the fat. The emulsifier will grab the particles of fat and keep them from coalescing and so keep them in solution. Look at mayonnaise recipes for examples of this technique though, of course, you don't want as much air worked into your dish.
I would mix a small amount of lecithin into the milk and whisk it quickly as you drizzle in the butter.
As for the vodka- I don't use alcohol and can't predict how it will behave. If your milk is cold then you shouldn't have a problem with curdling and should be able to mix the vodka directly in with the milk. I fear that if it went directly into the butter that there would be enough liquid to make the emulsification difficult.