I would take the job and cut short your leave - see if you can negotiate it to part time- and keep fingers crossed it takes a while to open up. Often start dates will be a month from offer anyway despite how urgent they often say it is. I know several times I have been told how desperate are for you to start etc but then the HR wheels take time to turn.

I couldn't do the travel for three hours either, and for me personally it makes a big difference that your mum is able to look after DD2 - in your shoes I would find the decision harder if had to use childcare but I probably still would do it for the long-term gain.