The phenomenon you mentioned is very common at present. The difference is generally that mothers are strict with their children, and grandparents are distressed to protect this situation. This practice of the elderly is understandable in reason. As the saying goes, "every generation of relatives" makes sense, but it may not be good for children's growth. Often have the psychology of having an umbrella. Even if you know that you are doing something wrong, you will have no scruples. Over time, you will develop some habits that are not conducive to growth, such as life.
The best way is to communicate with my mother-in-law and explain these truths to her. I'm sure she will support your education method, because she loves her children, and of course she hopes her children will win in the fierce social competition in the future, which is inseparable from successful family education. I hope it helps you. Thank you.