mnich

Feeling out of control of your child’s situation is so hard and it is especially frustrating when people don’t respect your wishes. From similar experience personally, I would suggest a few things:
1) It is your MIL, so boundaries and difficult communications would be best handled by your wife. After you two have come to a decision on how to move forward.
2) it sounds like you may need to be more firm about your boundaries and requirements for them, and consider framing it as “if they would like to be considered as child minders for you…XYZ are our non-negotiable requirements”
3) pick your battles on what are non-negotiables. When they aren’t in your care, you just don’t have full control and letting go of that is hard but helpful.
4) lastly, when you are struggling with their lax and silly ways with your child…don’t forget that the vast majority of your child’s time and raising is within your home and it is there that you have control and that they will gain their values etc. While it feels like they will be forever ruined…they won’t. You’re a good parent and they will learn the most from you.