i suppose you could fit it an inline hard water filter inline into your hose, but you'll want to keep it stable and not drag it round with the hose..... maybe fit it right at the tap end of the hose. i presume you'll be using a regular hose with a connection onto your kitchen tap......
i would make up a hose starting with your tap connection, then give it about 1 meter of hose pipe, cut the hose and put the end in a jar of boiling water for 2-3 mins...this will make it easier to fit over copper tube..... get a peice of 15mm copper tube about 6" long and insert it about 3" into the warmed up end of the hose pipe. clamp it on using 1 or two jubilee clips. the other 3" of copper left sticking out the hose pipe can be inserted into the filter ( note the direction of flow marked on the filter) . the filter should have a 15mm nut and olive compression type of joint so just push the copper right in and tighten the nut. do the same on the other end of the filter only this time, fit the long length of hose pipe.
make sure all the nuts and jubilee clips are good and tight.
finaly, i would coil up the first 2 meters of hose, which include the filter and neatly cable tie it into a gentle coil. this coil can safley sit in your sink, avoiding any knocks, snags or undue stresses.
i dont see why this wont work. obviously, it will impair the pressure of the water, but only a little. the filters are cheap, maybe a ten or 20 quid ( i dont know exactly, i dont pay for them i just fit them...).from any plumb center or plumbers merchants.... it should last a very long time.
we dont have hard water were i live, so i wont be needing to do this myself..... so let me know how you get on with it.