Will the DSP differentiate between house sale proceeds (which are temporary until another house is bought) and savings or will they just assess the proceeds as savings?
No it shouldn't be assessed if it's explained to them and you have proof of sale (funds origin) etc., but there'll be a time limit. Check with the Social Welfare.
It sounds to me like savings. It is not as if you are in temporary accommodation waiting to move from one house you sold to another you are buying. It sounds to me like you are choosing to live in rental accommodation (and have done so for the last 2-3 years). You also sold an asset in the past and have savings, which if I were DSP I would expect you to declare. Sorry the time line is too long for it to be temporary.