She has enough on her plate without leaving her home on his orders with nowhere to go and no furniture.
Don't let him get away with this. They are HIS children, not just hers. He has an obligation to do his share. Nag her to go at the very least to CAB and see what they say, even better to have her half hour with a lawyer who has experience of marital breakup.
It will be hard for her to do this, but even harder to cope alone with her children without any input at all from this louse.
Is he playing the old "I paid for the furniture" card? Well, she is entitled to half his money and half the contents of the home. If he won't contribute voluintarily, he needs a legal push. Just a stiff letter from a lawyer might do it. That kind of bully has more respect for male power than for female pliancy.