Ven. Pa Auk Sayadaw explains here that clinging leads to suffering, and in this case, this includes clinging to family members, clinging to their beauty, clinging to the beauty of possessions etc.
Being worried or concerned or obsessed about one's family members or their health, wealth, looks, possessions, career, future etc. are different expressions of clinging. The beauty of possessions is also impermanent.
This can be seen in SN 55.54 below.
The idea is to accept that one's own health and life, and one's family members and their health, wealth, possessions, looks, career, future etc. are all impermanent.
How is this related to karma? Well, clinging and craving leads to the three poisons of greed, aversion and delusion. The three poisons will lead to committing bad karma.
For e.g. I like the beauty of my plants, but my neighbour damages it, leading to my hurting or insulting him. I would have aversive emotions towards my neighbour because he disrupted my greedy emotions towards the beauty of my plants. These aversive emotions are suffering. Then this leads to the delusional mental state of rage and anger, leading to the bad karma of somehow taking revenge on my neighbour. Bad karma of harming my neighbour will somehow cause me further suffering in future.
So starting from craving and clinging, this will eventually lead to suffering.
Mahānāma the Sakyan heard about this. Then he went up to the Buddha,
bowed, sat down to one side, and told him that he had heard that the
Buddha was leaving. He added, “Sir, I haven’t heard and learned it in
the presence of the Buddha how a wise lay follower should advise
another wise lay follower who is sick, suffering, gravely ill.”
“Mahānāma, a wise lay follower should put at ease another wise lay
follower who is sick, suffering, gravely ill with four consolations.
‘Be at ease, sir. You have experiential confidence in the Buddha … the
teaching … the Saṅgha … And you have the ethical conduct loved by the
noble ones … leading to immersion.’
When a wise lay follower has put at ease another wise lay follower who
is sick, suffering, gravely ill with these four consolations, they
should say: ‘Are you concerned for your mother and father?’ If they
reply, ‘I am,’ they should say: ‘But sir, it’s your nature to die.
Whether or not you are concerned for your mother and father, you will
die anyway. It would be good to give up concern for your mother and
father.’
If they reply, ‘I have given up concern for my mother and father,’
they should say: ‘But are you concerned for your partners and
children?’ If they reply, ‘I am,’ they should say: ‘But sir, it’s your
nature to die. Whether or not you are concerned for your partners and
children, you will die anyway. It would be good to give up concern for
your partners and children.’
If they reply, ‘I have given up concern for my partners and children,’
they should say: ‘But are you concerned for the five kinds of human
sensual stimulation?’ If they reply, ‘I am,’ they should say: ‘Good
sir, heavenly sensual pleasures are better than human sensual
pleasures. It would be good to turn your mind away from human sensual
pleasures and fix it on the gods of the Four Great Kings.’
If they reply, ‘I have done so,’ they should say: ‘Good sir, the gods
of the Thirty-Three are better than the gods of the Four Great Kings …
Good sir, the gods of Yama … the Joyful Gods … the Gods Who Love to
Create … the Gods Who Control the Creations of Others … the Gods of
the Brahmā realm are better than the Gods Who Control the Creations of
Others. It would be good to turn your mind away from the Gods Who
Control the Creations of Others and fix it on the Gods of the Brahmā
realm.’ If they reply, ‘I have done so,’ they should say: ‘Good sir,
the Brahmā realm is impermanent, not lasting, and included within
identity. It would be good to turn your mind away from the Brahmā
realm and apply it to the cessation of identity.’
If they reply, ‘I have done so,’ then there is no difference between a
lay follower whose mind is freed in this way and a mendicant whose
mind is freed from defilements; that is, between the freedom of one
and the other.”
SN 55.54