I am a devout Buddhist who has studied Buddhism for more than 20 years. After looking at your lover’s situation, I feel that she is also very devout, and it is precisely because of her piety that her behavior is a bit extreme. I hope you can communicate with her rationally. What follows is for reference only.
It is really inappropriate to ask children not to eat eggs and milk. Buddha never did this. After Buddha became a monk, his son Rahula lived like ordinary people during his childhood and youth.
People who believe in Buddhism should be tolerant and compassionate, and should not impose their own wishes or beliefs on their family members. Even the Buddha was not like this, let alone us ordinary Buddhists. "The Biography of Sakyamuni Buddha" records that after the Buddha became a monk, he was respectful to his family members and did not force them to become vegetarians. They are not forced to believe in Buddhism. It is also illegal to force children to believe in religion.
People who believe in Buddhism must not force their family members to believe in Buddhism. Some Western cults recruit people to join them all day long, which has disgusted the Chinese people to the extreme. If Buddhists do this, it will make others hate Buddhism and destroy people's wisdom and life. Buddhists should think deeply.
Buddha only taught not to kill, but he never said that lay people should not eat meat. Could you please ask her to find scriptures to see if there is any scripture that says that lay people should not eat meat? Since the Buddhist scriptures do not say that lay disciples must eat vegetarian food, it means that the Buddha allowed lay disciples to eat meat. Buddhists should follow the Buddhist scriptures.
Moreover, Buddhism allows drinking milk. This is recorded in many Buddhist scriptures. The Buddha ate the chylo offered by the shepherdess and meditated under the bodhi tree to become a Buddha. This period of Buddhist history is known to almost every Buddhist. Chyle is milk for cooking porridge. In addition, the Vimalakīrti Sutra also records that the Buddha drank milk when he was a boy. Please find this passage from the "Vimalakīrti Sutra" and show it to her. She believes in Buddhism, so she will definitely not oppose it, right? .
In addition, medical evidence has shown that long-term vegetarianism can lead to a lack of vitamin B12 and a lack of vitamin L-carnitine. These two vitamins are only found in animal foods and may cause disease if they are deficient for a long time. Please look up the information on these two vitamins and the dangers of deficiency on the Internet and ask your lover to read it. I think she will change her attitude.