I don't know if you are misreading the situation; only God knows your friend's true feelings. It's possible, for example, that focusing on her dog's death keeps her from thinking about the greater pain of her husband's death.
But sadly, it's also possible that your observation is correct. Sometimes people do love their animals more than their spouses, or other people who are close to them. Perhaps a relationship is difficult or has grown cold; perhaps someone simply finds it easier to meet a pet's needs than to bother with those of another person. The Bible talks about a time when, "Because of the increase of wickedness, the love of most will grow cold" (Matthew 24:12).
However, it shouldn't be this way. We need other people -- and they need us. I grew up on a farm and have had pets all my life, and I still enjoy their company. But God did not intend for them to be a substitute for other people. In the Garden of Eden, Adam was surrounded by all the animals God had made, but that was not enough. The Bible says that God declared, "It is not good for the man to be alone. I will make a helper suitable for him" (Genesis 2:18).
Pray for your neighbor, and do what you can to be a friend to her. Most of all, encourage her to find her hope and peace in Christ, who alone can turn our darkness into light.