hi ron! we have the same circumstance; i'll be applying next week, same type of accommodation and we have a 3 year old too! but don't worry, i think we'll be ok.As long as the landlord gave you an approval on living there with your family. your house will be counted as 2-rooms (1 bed and 1 living room).
My sister in law applied for settlement visa last year with her 5 year old in tow, they're renting a 1 bed flat too, and they got their visa.
here's more info: http://www.ukvisas.gov.uk/en/ecg/mai...ation#18172733