Sorry but you will just have to wait.
What is it with everyone thinking they need a 3 bedroom house if they have more than 2 kids? You don't! Kids can share and if they are different sex you can split a double room into 2 easily (my mum and dad did this for me and my brother) and have bunkbeds! They only have to sleep in a bedroom, not live in it.
Before I was born my mum had to live with her husband and 3 children in her mum and stepdads 2 up and 2 down house (which nan and grandad owned) for about 4 years before they were able to be allocated a council house.
Dad worked all the hours he could in a hard manual job and mum worked as a cleaner and went out cleaning when dad got home. (nan and grandad were disabled so mum helped look after them as well).
Nan and stepgrandad lived in the bottom rooms and my mum and family on the top floor (plus they were charged rent and food and bills by nan who was the tightest woman alive).
They had to do this as there were no private renters in the area where they lived, couldn't afford a deposit on a house and most private landlords would not accept families. (this was back in the 60s) and council housing was a 5year+ wait.
So think yourself bloody lucky you have a roof over your head and its a 3 bedroom house so there is plenty of room (1 bedroom for your mum and husband/ partner, 1 bedroom for you and your partner and 1 bedroom for the kids) and its only a 2 year wait.
Try sleeping 2 adults and 3 children in the same room and then you will have every right to complain about being cramped.