I can't see anything wrong with TUI's flightpath.
There's a problem at Funchal in that the airport location and terrain prevents the typical long straight approach towards the runway that you see at most airports.
That means for instrument approaches you fly a track displaced to the east of the runway centre line, done deliberately to avoid the high ground on the island to the north east of the airfield.
It's only when the aircraft gets to a radio beacon/GPS waypoint on the headland near d'Abra Bay, and also only if they are visual with the runway, that the aircraft can be turned right, onto a more westerly track, towards the coast, to line up with the runway.... OTOH if nothing is seen at that point then it's a go-around and basically a turn to the left to keep clear of land, which is what TUI did.
TAP flew the same easterly trajectory as far as the beacon/GPS waypoint, but then they turned for the airport so it looks like they simply got lucky with timing and the weather. By the time TUI had a go the weather was outside limits again.
HTH.