I feel sorry for the aunt. It's all very well saying that she should find a way to feed and house the children for a weekend, but if she lives in a small flat, then she may literally not have any suitable space for them to sleep in, or bedding etc even if they could sleep on the floor (which is not going to be pleasant for the children, when presumably they have proper beds at mums).
Feeding 4 children for a weekend is potentially a lot of money, if she doesn't have much food in. If it was just her, I imagine she would prioritise the children, but most parents won't be willing to prioritise their nieces and nephews over their own kids in terms of feeding them, paying bills etc.
Plus, I guess it is in the back of her mind that actually the mum may not come back on Monday, and she is stuck with the responsibility longer term.
I agree with asking the police to do a welfare check on the mum, actually. They may not be willing to, but if this is very out of character for her, I'd be genuinely concerned about her mental health. It's not impossible she wants the children out of the house because she is having a mental health crisis.
Ideally, I'd think maybe the mum should leave the family home for the weekend, and allow the dad to stay there to look after the children. But I understand there may be lots of reasons she doesn't want to do this.
As others have said, I doubt the father has chosen to be in this situation. But yes, he should try to come up with a better plan for his weekends long term. However, short term, I don't think it is actually unreasonable for someone who is newly homeless to say "sorry, I can't have the kids this weekend, I've got no money and I'm literally homeless". The resident parent wouldn't be in that situation, because they would be found some kind of emergency housing.
I do actually think social services ought to get involved on some level, but I also know they're very overstretched.
Has the sister in law got back in touch with them, explained the mum cannot be contacted and the children have nowhere to sleep tonight?