Personally, I would put the house back on the market straight away, and write a letter to the builder, recorded delivery, stating that you have done that, that he has been given reasonable time (over 6 months!!) to proceed to exchange, and that unless he now exchanges contracts within 14 days, you are withdrawing from the sale.
As your mum has already lost the house she wanted anyway, she has nothing to lose as if he gets a wiggle on and buys quickly, she will be a buyer in a buyer's market, and if he withdraws, it's back on the market with the enhanced attraction of that (presumably) outline planning permission.
Good luck.