If you are lucky to get to a second series of a spin-off then you have to start fleshing out the supporting characters so that it doesn't feel like it's all on the head of the character that has been spun-off. This is one of the fatal errors that 'Joey' made.
While Martha still remains a bit 2D, the writers here do seem to be making a go of trying to achieve this.
So we have a rather sweet ongoing plot involving Martha's mum and online dating, we get to see a bit more about Esther's past, and even Humphrey himself is given a wonderful opportunity to shine in a dramatic moment.
It's things like this that elevate the show beyond the rather rigid format of its parent programme ('Death in Paradise') and offer us a bit more to invest in.