Right. Not brilliant at writing letters but I'd do something along these lines.
Dear XXX
I am writing to put a formal request that the property XXX be provided with a single storey extension to provide an additional bedroom.
The property at present has 3 bedrooms and a reception room. As you will be aware I have three children and my husband Peter is currently at home (insert description of the care he has at home - the equipment and so on). Clearly it is necessary for Peter to have his own bedroom, and that room can be used for no other purpose due to the nature of the machinery and facilities required to keep his life-threatening condition stable.
As a result the two remaining bedrooms are crowded with myself and our three daughters. This situation, as I am sure you will appreciate, is not ideal and causes a great deal of stress for all concerned as my daughter (eldest, middle, youngest??) is unable to sleep in a bed and none of my children have adequate space to store their clothes and possessions and play in comfort.
Clearly it is considered by health professionals and of course us, his family, that Peter should ideally be at home with his family. However, we wish to limit the impact of his on-going treatment on his children as much as is possible. After all, this is a stressful time for everyone, including the children.
I appreciate that there is a desperate shortage of larger houses in the area suitable for our special needs. With this in mind I would like to suggest that our current home could be made more habitable if a single storey extension was built to provide a bedroom for Peter. This would enable the remaining 4 members of the family to occupy the existing 3 bedrooms.
It could be argued that in improving your existing housing stock there would be a long term benefit for your housing association aside from the shorter term benefit to our family.
You are no doubt aware that this is a pressing need at this current time and I would therefore appreciate your prompt consideration of this request as a positive response could make such an enormous difference to our quality of life.
Yours XXXX
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Sorry if this is not relevant to your particular situation - best I could come up with while the dcs are on my case