First, you can’t force “non attachment”. Any attempt at that is a way instead of getting strongly attached to some conceptual notion you have of what non attachment is. If that happens then you are in an even worse situation than you were before. You think you are practicing non attachment. But instead you may be practicing indifference, coldness of heart, a strong focus on yourself over and above everyone else, and now that you have called it non attachment - how can you ever do anything about it? You are just reinforcing this closed in coldness of heart whenever you practice what you think is non attachment in an attempt to do something about it. You may notice at some point that it doesn’t seem right, like there is a barrier between yourself and others, but you still can’t do anything about it. It may be very hard for someone to get out of such a trap.

Instead non attachment is something that you can reach through compassion, through opening out to others, through somewhat less focusing on yourself and your wishes and goals, through humour, letting up a little. Others can often help you in ways you can’t yourself.

So - yes compassion and loving kindness towards the closest people in your life is part of the path of non attachment. And the main difference between the attached and the non attached response in this Buddhist sense is that it is less claustrophobic, it’s helping both of you grow, it’s open to others as well, what you are doing may have ripples well beyond the immediate situation you can see. And it’s a learning process so part of it also is being kind to yourself as well as others. Like a toddler learning to walk, you are going to fall over, over and over. But you just pick yourself up and keep going. So that is part of non attachment too. Not being attached to your non attachment, and accepting that you make many mistakes and being kind to yourself.