Firstly OP, I think the text you sent her was worded perfectly, and would also have been miffed at her response.
Moreover, you've done something to try and help, which is commendable, but unwittingly got yourself into a pickle in the process.
You sound very much like myself, a people pleaser, and fixer of problems, but I've learned this isn't always a good thing, for either party - not everybody wants or needs help or fixing and then when you lend or give it, it can wind up biting you in the arse, for want of putting it more eloquently and you find yourself too overly involved in other people's lives, at a cost to your own, on emotional and time levels (plus, invariably, sometimes at a financial cost to yourself too)
Chalk it up to experience, try and learn when to take a step back (I'm still very much working on this myself) and lastly, well done for how you stood your ground - although as a side note, whilst she may have been slightly naive to the £45 per hour cost, it maybe hit a nerve, I don't know whether you needed to mention the monetary cost in order to drive the message home, however, no matter, not berating you just mentioning it as it maybe put her back up a bit, even though it wasn't your intention.