Taking a washing machine from a mobile home?

My parents are currently considering selling their mobile home to the site owner where the mobile is at the minute. They paid 70,000 euro for it 8 years ago. They are currently being offered only 25,000 (sign of the times i suppose)
Anyway, when they purchased it brand new, it had a washing machine and fridge in it. They are wondering can they take the machine with them without consulting the purchaser? Could they get away with this?

The fact you are asking could they get away with this suggests that they/you suspect that it is the wrong thing to do.
I'm not familiar with mobile homes but I suspect they come fully fitted which would include the washing machine.

Leave the machine ..... it's not worth causing aggro over it.

If they own the mobile home, then they own the washing machine.

Could another family member not take the mobile home from the parents rather than sell it at such a big loss?

If it is sold 'as is' with the items, then they cannot remove. If the intending purchaser is told that they are not part of sale, then they can.