I think divorce should be the last resort.
I also think you're on to something, the communication between the 2 of you as a couple is seriously damaged.
Find some time to talk to each other without your baby and without your mother in law to figure out the root of your problem
- are you both tired from juggling work and parenting,
- is there a problem with HOW the 2 of you are talking to each other, are you both angry at each other all the time, why?
If you feel that your mother in law might be adding to the tension, try to communicate with him so that he understands that HE has to be the one to set the boundaries with her