My wife and I are barely speaking after an argument and the whole house feels heavy. How was the Prophet with his wives when there was tension?
Brother, the heaviness you are describing, the silence at the table, the careful stepping around each other, is not proof that something has broken beyond repair. Two people who live close together will sometimes brush against one another the wrong way. What matters now is how the two of you come back.
Look at how the Prophet (peace be upon him) lived inside his own home. He read the heart of his wife closely enough to say to Aisha:
“I know when you are pleased with me, and when you are angry with me.”
The Prophet (peace be upon him), Sahih al-Bukhari (5228) · meaning
Notice what he did not do. He did not pretend the tension was absent, he did not withdraw and wait for her to repair it, and he did not ask her to hide what she felt. He noticed, and he said so gently. Much of an argument loses its heat the moment the other person feels they are being understood rather than out-argued.
And when the air needed clearing, he brought lightness instead of long speeches. Aisha herself reports the races between them:
“Aisha said: I raced with the Messenger of Allah and I outstripped him. Later, when I had grown fleshy, I raced him and he outstripped me, and he said: This is for that.”
Aisha (may Allah be pleased with her), Sunan Abi Dawud (2578) · meaning
Those who study marriage in our own time have arrived at something the Sunnah showed long ago: the marriages that last are not the ones without arguments, they are the ones where a small gesture offered by one is taken up by the other. The Prophet (peace be upon him) was practising this repair fourteen centuries before anyone wrote it down.
So do not set out to win the argument. Set out to reach her. A cup of tea placed by her hand, a memory only the two of you share, a light joke about something small, these are the little races across open ground that lift the weight from a house.
One small step: Today, without reopening the argument, offer your wife one small warm gesture, a cup of tea, a shared memory, or a gentle joke, and let that be your first step back toward her.