bip32 hd wallets – How may you detect if two prolonged keys have the identical root non-public key?

Say I derive three prolonged public keys¹ (regular mode):

Dad or mum:

Pubkey: 035f743ee7d73d27e8c80f6b2458e6d4e2a45f3d7dd35c4e4d84ff3d939d09f40c

Chaincode 71d145eec8d031b39107cb7cb9641cc1e8169b6a25b489b157a0af2197717970

Youngsters:

Pubkey: 0317365d2ea4aa79e731fd4f0f6d60bf0ef75a35189a647667eebc9c7323d304d0

Chaincode 9cb9a9fe6e57b62f9a7970649d8dc4633fd9d4b5777a1397a275bd30a88c3111

Pubkey: 0230cdc8f7b84c0998ec182777d9d1f35ea45fe7620e979862c7025b18162108cb

Chaincode 44b54106ea0720a1ac226d598b89297dfe8efd2b7abf75c88761aa6df9c2886b

If I’ve any two of those three (child-child or parent-child (not understanding which is father or mother)), is it doable to detect that the keys are associated? How would it not be completed?

If not, what additional data could be required. The kid indexes? Signatures from a shared root non-public key?

See additionally:

ELI5: What is the distinction between a child-key and a hardened child-key in BIP32

BIP32

_{1: I used this most glorious write up to create these.}