I suspect the 'build a case' idea stems from a breakdown in relationship going back to before Christmas, when the OP asked for reduced working hours and was refused.
We're picking up on the anger that's coming from the OP, and seems ridiculous when it's about a few texts that she could easily stop - but I'm thinking the anger isn't really about the texts but has been brewing for months. After all, the texts have only been happening a few days from what's been said here!
Care agencies as a rule are notorious for treating their employees badly, and their 'service users', which encourages the abuse levels which happen. There is a massive business opportunity for someone who creates an agency that respects and cares for their workers and clients... Good carers will flock to a place that values them, and clients will be desperate to have the reassurance that a good and non abusive, non neglective carer is not because the individual is good, but that any carer sent will be of this quality and ethics. Anyway, I digress!
So I wonder if there is more to the story than a mix up with texts. I also think that the OP needs to check the legal situation very carefully, as usually agencies skirt the law carefully and although they may have treated you badly, it may well not be covered by the law.
You need to find out whether there is any point in making your life and your babies life more difficult, dwelling on a bad situation in the past, and nursing a grievance which harms your own well being but potentially no one else's. It's easy to get stuck in this attitude, but it can be the better thing to let to of your anger, and need for restitution or vengeance.