Probably a totally hair brained thought, but with this family, who knows?
Incident at home of NS/DN, call in DS to save the day. Dress NS in Tia's clothing, admittedly with a push 'em up bra on, ensure she is seen on the Co Op's rather bad CCTV (why are there no other CCTV pics of Tia travelling from mum's to gran's?, has anyone checked the street/tram CCTV's for NS that day?, granted she could be in a taxi or a car, and changed into Tia clothes later). This would also explain why NS's phone is at gran's house.
After the initial plea, and a couple of house searches, they may have thought that gran's house was off the radar - smuggle body in, and hide in loft.
Wash the clothes like crazy to rid the majority of NS's DNA - although they would obviously share some DNA, if questioned, just say they shared clothes sometimes. Hoover like billy-o, to drown out any chance of conversations being heard by neighbours as walls are paper thin.
DS is a bigger fish in whatever game, and also apparently less addled than SH, so SH will do whatever he is told to maintain the first bit of stablelife he has had in years.
Yes, it's a very long shot - but I too think they went from 0 to grieving a bit too quickly, initially it would be more panicky and feelings of helplessness tears.