Alternatives milk sources

Your sims can order groceries from the refrigerator, and milk and eggs are in the list available to buy.
You can also have them visit the grocery stand in Henford-on-Bagley, milk and eggs are also sold there.

What I did in my game is have a sim household produce all of the milk and egg varieties and then put them in a LICE Retail Freezer on a Retail lot. It's a big grocery store, which sells every food ingredient item in the game. Then I sold the retail lot so that it is unowned because unowned retail locations automatically restock between visits.
The supply a sim can buy out of the LICE Retail freezer is also unlimited, even if you only put 1 of the item inside in the first place.

The end result, all of my sims can buy any fruit, vegetable, dairy product, etc. at the grocery store. I even made custard, mayo, jams, etc. and have all those for sale at the store. It feels just like a real store, and all of my played sims visit it.

I use the "Simple Living" lot trait on all of my played households, and make my sims who don't raise/grow their own ingredients go grocery shopping. It's good.

There are mods which add a lot of new ingredients to the game so there are probably mods (other than the cow plant one) with alternative milk types, but the problem is that they wouldn't be tied to any of the game's recipes without the mod being a total overhaul of cooking.