Think about what the separate sentences are saying in this passage. In sentence one, the speaker is not hitting, not striking, but taking her face in hand. The second sentence adds that this is being done gently. Apparently there has been anger and screaming at some previous point, but those emotions and actions have not produced the desired effect ("were not working"). Therefore, the speaker decides to try a different approach toward achieving whatever goal he has in mind.
Remember the saying, "You can attract more bees with honey than with vinegar"? That's what is happening in your quote. Fighting and arguing is not producing success, so the speaker is trying a loving, gentle approach.