My husband and I both practices different religion but we made it clear that we will not influence each other. Recently, my MIL wants my kid to be involve in their religious ritual which I am not keen for my daughter to. How can I reject her without offending or hurting my MIL? (as a respect, not mentioning any of the religion)

If you're not keen for your daughter to participate, just tell your MIL that you don't want your daughter doing that. If it's hard for you to say it, get your husband to do it. Most of my relatives are Buddhists and they practice the offering of joss sticks. My mother was a Christian and I could stand aside and not offer joss sticks. There are other ways to show respect without having to participate in the ritual. Since you don't want to influence your daughter, do not let her participate in the ritual. However, you also have to note that if you don't want your daughter to take part in rituals related to their religion, you shouldn't let your daughter participate in any rituals or practices involved in your religion to be fair.