Oh OP I feel for you,. it's so hard getting this right.
On the one hand, you want to 'lay down the law', I suspect, because if this week it's her ignoring your instructions on spectacles, I presume you are imagining that soon it will be a slippery slope to other bad behaviour, which your MiL is going to allow in defiance of your instructions.
She should never have said 'I'll just do it behind your back anyway'. it IS subversive, rude, disrespectful, and it diminishes your position as the child's parent. it is not unreasonable for you to ask caregivers to respect certain rules. She is not the fucking messiah.
HOWEVER, in the interests of the long-game, I think you are going to have to compromise a little. Children don't actually expect 1005 consistency of approach between caregivers, and they come to realise quickly that what they might get away with at granny's, they will NOT be allowed to do to mummy, or in front of the nanny.
I also think you need to pick your battles here. We started off with a long list of non- negotiables re food/drink/ screen-time/general discipline (e.g. we don't practice reward/ punishment driven parenting, and the GPS couldn't and still can't fathom this, so we've let it slide outside of the home.) Over time therefore, we have whittled our 'wants' right down to a couple of bare 'needs' (no fruit shoots/ fizzies or sticky/ hard sweets, no smacking, minimal bribery.) Even then, I suspect half of our requests are ignored, and we have a kind of 'wink wink' understanding about this now. The thing that would make me lose my shit was when MiL would try to give my EBF baby formula in a bottle behind my back. Having got past that charming incident in our relationship, the thought of my toddler getting sticky lollipops doesn't quite affect me so much....
I'm afraid you DO need to develop a thick skin and a bit of sense of humour when dealing with GPs. It does generally get easier.