Responding with love doesn't mean giving in. It means letting them know, you hear them, repeat back what they are saying to you. You may realize, they have a valid reason for their position.
Also let them know you see they are frustrated, hurt, sad, angry and that you will be by their side through it. Help them learn how to work their way through these energies and how to come back to peace and calm, which brings clarity, which lets solutions to problems pour in.
Teach them the Ho'ponopono prayer, the Lords Prayer, how to calm with slowing breath 5 counts in, 5 accounts hold 5 counts out 5 counts hold- repeat. Be the example when you are about yo have your own meltdown. They are watching how we handle stress and difficult people.
Many parents play the silent game with their kids when they act up to get them calm down and come around. Its damaging to make them go invisible to you. The rejected child goes into shame and hiding. What you get after that is their mask.