No Hot water to Shower and Taps furthest away from hot water tank
1) The red line that is teed into the blue line after the check valve could be used as a recirculating line to provide almost instant hot water to all the hot faucets. Make sure that you add a check valve in that line so you do not get reverse water flow when a faucet is turned on. 2) The supply line to the heat pump should come from the bottom of the storage tank so it utilizes the coldest water to be heated,  and not come off the hot supply from the storage tank.  3)The hot discharge from the heat pump should go to a separate tap near the middle of the tank if one is available. If a separate tapping  connection point is not available I would then tee it into the cold blue line at the tank supply but after the check valve. 4) I believe that a circulation pump is required in the heat pump line sized as per the heat pump's instruction sheet. 5) One last thing, if the red line I mentioned in item #1 is for a  recirculating line to insure almost instant hot water at each faucet it can stay as is and you will need to install a pump  on that line to circulate the water (buy the smallest pump you can) Mine is a B&amp;G NBF-8S  103257LF 39 watts. 6) you said that you did not show the cold supply (mistake).