Yes you are allowed to travel for a house move, My step brother did this last week. The new house would then be your permanent residence, but your son, and You as his Carer, whole then be allowed to travel back under the rule of ‘Travelling to attend a medical appointment and or gain Treatment’. You would just need to carry the Medical evidence such as a Hospital letter or Appointment card to show that this was the case should you ever need to show proof to the authorities. Should you need to, you could also stay overnight in a Hotel during your visit, one of the few circumstances where Hotels are allowed to accept bookings from Guests during lockdown.