agree with wwaswas if the slabs to fall towards the garage you need a drain the whole length of the garage or re-lay the slabs to fall towards the grass, both could cost a bit. maybe worth checking the drain isn’t blocked with bike washing detritus first and hence not draining?
it may be possible that if you report to the council they could enforce her to clear up her overgrown garden and hence drainage which will likely be blocked
also, if the water is definitely coming from her side and she’s not wanting to help sort it, you may have a case for claim on her part to help re mediate the problem – as she’s clearly not doing anything to stop water running off her land onto yours which is then damaging your property. you might want to discuss that with a proper legal person tho before sending the bailiffs/brother in law round… :D