I didn't know they didn't have to house you locally, I wrongly assumed if you had been in the area 6 months that council had a duty as that's what it says on the website however I guess that means they have a duty to give you SOMEWHERE not where you choose.
Well, of course that's what it means, did you think you were just going to move to Bognor, rock up at the council and choose whichever one of their 3 bedroomed houses you fancied after six months? Sorry if that sounds harsh, but I'm incredulous at your lack of thought about this.
If you're on the list (and you have to get on it in the first place) and bidding for properties, some categories of applicant have the right to refuse if an offer is made and stay on the list, some do not. For example if a disabled person is offered an unsuitable property I think they can refuse it. If you are being made homeless, ie, if your landlord is evicting you, you must take the first property offered to you or be removed from the list. There will also be many, many people ahead of you, which is why people end up in B&B accommodation - which I presume you think is like being on holiday? It's not. You get one room in a shared house for the family.
To get on the list in the first place you have to go through an application process and then wait to be assessed before they give you a banding. Only then can you bid for properties, and only those applicable to your band. Like I said, it took my local council 11 months to assess my application, there's such a backlog of people applying - and I'm disabled and in need of a ground floor place (which I am currently not in).
Please, do your research before you even consider this. You already have a home, and there are thousands and thousands of people in far more need than you who are waiting years to be housed - the number of bids on each family sized property in my area can run into hundreds - so I'm not sure why you think you'll get somewhere after six months.
The thought of someone willingly subjecting their children to a miserable existence in one-roomed B&B accommodation just because they want to live near their mum is horrific.