N.K.
It sounds like you're in a tough position. being a single mom and having to go back to work so soon must be really hard. having a baby is such an arduaous and lifechanging event. my baby has just turned 1 and things have gotten a little easier in many ways, especially with the sleeping.
i am quite fond of attatchment parenting, which is only one way to approach the whole process. in my opinion it is a good one. it advocates close contact and unconditional response in the first 6 months of life, at least as often as you can. Even other research that i have done has pointed to the fact that an infant under 2 months(some say as long as 6 months), especially one as young as 6 weeks or less, is not capable of having its needs conveyed to you in any other way than crying and that they are simply too young to be crying in order to control you. when their crying is not responded to in some way there is less sense of safety for them.
i am not saying any of this to scare you. plenty of us were left to cry it out, or to cry ourselves to sleep, and we are okay as adults. no matter what, your child only expects you to do the best you can, and if you give him all the love and attention you are capable of when you are with him he will grow up well.
just the same, i agree with you that leaving and knowing the person watching your precious little one refuses to comfort him would be heart wrenching. i am not sure if it is possible to change the way your mother would be with him if that is the way she believes is best. try and talk to her, or find an alternative sitter( which i know can be hard to come by). if there is no other option, i would watch him over the first days and weeks of your new sitter relationship and trust your gut. if he seems worse off, or upset or like he is trying to tell you something, or if you have a bad feeling in your stomach, try to consider any other options there might be, like maybe doing some day shifts, so he is not uncomforted all night, but is with your mom during the day when he is maybe in less need of comfort.
regardless of what i believe or anyone does about the right way to raise a child, one thing is for sure - you are your baby's mom, and your baby can communicate with you and your body in ways that even science does not fully understand. trust your senses. trust your baby.