People who actually need three bedrooms struggle to get them. If you are going to pretend to be single to be awarded a house then I really can't see one adult and one child being given a three bedroom house. If you're wanting to proper lie and all live together but say you're in a room each you'll still be unlikely to get offered one and might find proving it a pain in arse. A friend actually genuinely had split from her dh and he was living on sofa, she couldn't claim a penny because HMRC wanted solicitors letters proving they'd split, bank statements to show they were not sharing finances and living as a couple.
You might want to check the way the Council allocate houses anyway as many don't have "lists" as such, two councils near me have a system where you bid on a property and the person with most points/need will win it so to speak. So in theory an unpopular area could have three bedrooms properties you'd be given but then if it's an unpopular Are and families don't want to live there it's unlikely you'll want to either.
Someone else being on benefits and having a council home is irrelevant to your situation, you sound a bit entitled tbh and if you really think being on benefits is so cushty you're free to quit work and join people.
Can you private rent? You were willing to pay extra for a spare bedroom in bedroom tax (which wouldn't apply if you're not on benefits) House swap if already in council house?
FWIW some councils count a dining room as a bedroom so bare that in mind, I private rent and dh lost work last year and we had to claim benefits, it's a two bedroomed house but council came out to look and classed it as three because of the dining room and we had to pay extra.
You'd be very very very lucky to be given a house with bedroom for children who haven't even been conceived and even then they can be expected to share. My Sister has three daughters and even in an unpopular area count get more than a three bedroom home , (two bedrooms and a dining room which council class as third room)