Rant.. Should I quit my job to look after baby

The initial plan was for my mil to take care of my baby. However, after she temporarily stay with us for the past few weeks. I got a bit worried. She seems to want baby closer to her than me. Everytime I carry baby, she will want me to put baby in rocker or pass to her. Then when I want to wake baby for feeding, she will ask me let him sleep so she can continue to look after him. Yet she herself can wake him to play. Recently baby is also in the leap week so he clings to me. So, my mil was not happy about it and seems to blame me. Even compare him with my sil (her daughter) kid. I really very stressed with my Mil. I am thinking should I really let her take care. Will she make my son closer to her than me. #advicepls #firstbaby