I share the same experience. My "competitor" is the maid. Similar to you, I have decided to place my child in a childcare since my maid has decided to go home after completing her contract. Of now, I do not wish to engage another maid but I know I will be the maid and it is going to be very tiring, esp since I am a full time working mum. Now is still early intervention, so I hope it is still ok.
My friends have told me that not to worry, the child will know who's his/her mummy somehow. Kids are smart, they know who to go for what. Going to your mother-in-law is a source of comfort and I think it is still okay. The question is when you are without your mum-in-law around, does he still comes to you?