I 'do' pigs these days, but for most of my working life, I've 'done' dairy cows.
The whole 'farmers don't get a fair price' is no truer for farmers than any other small business owner. If you buy milk from a local organic herd it's about as 'good' ethically, as you'll ever get, but as dairy cows have been bred selectively for generations for attributes to make them suitable for intensive farming there is bound to be a trade off in quality of life. Even organic cows give more milk than their median suspensory ligaments can cope with and don't have good longevity.
Goats are less intensively farmed, but their milk tastes goat-y. And you still need kids for goats to make milk- they dry off just like cows do! If you have a house cow you can keep her producing milk for years just like you can with goats, but the volume you'd get is pitiful. Long lactation is stressful on the udder- they become more susceptible to mastitis-causing organisms. In this country bull calves are not waste, or veal, they are reared for beef. Even my low moral standards struggled with the New Zealand approach to dairying, which I suspect is where kcass' examples come from. I quit, I couldn't believe they treated their stock as they did.
For your house cow, you need a
Dexter.
Soya is GM, nearly everywhere except in the EU, so your soya milk would have to be organic, and grown far enough away from other non-organic soya. (Soya is permissible protein for animal feed, a much bigger market than for human consumption). And soya doesn't grow well in the UK, so think of those food miles.
Rice milk is yakky.
So, no, you can't get ethical milk, except from your mum.
Lots of cultures just don't drink milk. It's for babies, not grown ups!