OP you would be silly to give up a council home as they are like gold dust.
Your best bet is to accept it and then look for somewhere to rent privately.
I get why you’re so worried but I think you’ll be shocked at how many peados there are around, so never completely trust anyone with your children.
If you’re in a council/housing association property you are more likely to be around a peado as they are rehoused by them when they come out of jail.
On my small estate there were 3 convicted peados that we knew about (probably many more unconvicted ones) and 1 was harassing his victim so he was relocated 10 miles away through the council and the person they swapped him with was also a convicted peado.
So it must be a thing that they do.
Where ever you move to you are more than likely going to live near a peado unfortunately.
Imagine turning this down and either being kicked off the list or given 1 more chance and then next property is even worse!
It’s completely your choice but I was in temporary accommodation for years with not enough bedrooms so I had to sleep on the sofa, but fortunately it was a decent area.
And I know a couple of families currently in awful temporary accommodation as they’re full of people who need accommodation after coming out of prison or homeless on the street and there’s no room in the halfway houses.
And 1 is over an hour away and the other is 3 hours away from the childrens school as they literally just put you where there’s space.
They’re also much further down the list as their situation isn’t as immediate as someone who’s at risk of being homeless like yourselves (even though they’re classed as homeless).
If they were in your predicament they would snatch the councils hand off and then try to move.
Only you and DH can make this choice though and you shouldn’t feel pressured either way.