How about being straightforward and honest and just maybe you'll receive a straightforward and honest response in return?

How about accepting or challenging what they actually literally say as opposed to their attitude and your perception of said attitude?
i.e: "those cards won't mend anything attitude" is an observation based on your perception. Nothing about that statement tells us what was actually exchanged on either side.

The attitude you are percieving may not be reality at all, and idk either way because I'm just an avatar on a screen.

Maybe these people are just emotionally distant because that's how they are? Idk

My point is you need something concrete in order to know which action to take. Likewise so do we if we are to attempt to guide you...

So my advice is this.
Be blunt, be honest, no beating around the bush with gestures and implications.

Tell them you're sorry if you contributed in any way to whatever has led to such a rift, and ask them if there is a way to mend fences between you.

Clarity is simple yet powerful.