There are many different vegans with many different viewpoints. I am not vegan, but I come pretty close - I do still consume a limited amount of dairy, but otherwise I don't buy animal products. This is for the reasons you say - I don't want to support factory farming. I also have a limited amount of time in my life for investigating everything I eat, however - I don't honestly have the stamina to check every egg-containing product to see if it used battery eggs or not. I really don't have the time to check if the "free range" eggs I'm buying are really free range or if they have sneaked around the regulations and it's battery farming in disguise. It's just easier not to buy any eggs.

I will accept eggs from people I know who keep chickens - no problem from me there. I think that humans having relationships with domestic animals is fine, generally we both benefit - the animals because they are protected from predators, they get fed, etc, and us because we gets eggs.

Some vegans would not agree with me. Some vegans don't believe humans should keep any animals, including pets. I don't believe there's an issue with keeping some pets though. Domesticated animals wouldn't even exist without us... Like it or not their "natural" habitat is living with humans. You couldn't release all the dogs and expect that to be better for us or them.

She grew up on on a milk goat farm but never learned that goats don't give milk from the goodness of their heart?

Honestly at that point I think it's lower effort to just go vegan. You're already avoiding meat in every situation where you can't investigate the supply chain, so no meat at restaurants, fast food, friends' houses, etc. I guess if you really crave the taste of meat or something or if you live on a farm already I could see a case for it. For me, the case of going to the grocery and making a meal at home was always the easiest case to have a vegan diet (and avoiding all the extra prep and cleanup from preparing meat were nice perks), the parts that were actual hurdles were the convenience of fast food and not wanting to assert myself in group meals.

Personally, I figure that the tiny sliver of meat that's produced ethically can go to the tiny sliver of people with weird dietary restrictions, and to cats, I guess. We still need to see a massive reduction in meat consumption if we want to address the abuse that's rampant in the vast majority of meat production.