L.P.
T.,
I agree that your son cannot be spoiled at this age. "Giving in" to him at this age is simply another way of saying that you are 'meeting his needs'. You are teaching him that he can expect to have his needs met, even though he can't speak them yet. It teaches him a sense of security in the world and in his environment, which helps him to grow with confidence and trust in his mother/parents.
I also think he may be experiencing separation anxiety, which is tough right now if you have to leave him, but in a way, it is also a good thing, because in theory, he will grow out of it.
I do have several concerns, though. I agree with the others that your mother-in-law is quite probably trying to tell you that this job is too much for her. And not to point any accusatory fingers at her, but I would be cautious/fearful of how she is handling your son when he is non-stop crying, especially if it is taking her to her wits end...
Perhaps you and she just don't have the same beliefs about how to care for a 7 month old, as in maybe she doesn't feel he needs to be or should be held a lot, and maybe he is used to being held a lot by you, which may be something he is instinctively missing... the closeness of being held.
There are children born with all different types of tempraments, some are content to go for long periods without seeming to need much, then there are those higher needs children (I know, I have one) that just need more. Its not good or bad, just different... and different kinds of babies need different kinds of attention. Maybe your mother-in-law didn't have kids who needed much, or maybe it is just more traditional thinking from her generation that you can spoil a child by attending to them too much, which current research definitely does not support.
(A little side note is that my high needs baby is turning into a wonderfully sensitive, kind, and loving little boy, and although he needed to be held A LOT and needed a lot from me when he was a baby, he is no longer that way as he gets older... my belief is that he got his needs met as a baby and learned that he could have confidence in me and in himself, and that is evident in the way he is now blossoming...)
You didn't say whether you pay your mother-in-law to babysit for you, but if you do, I would seriously consider paying someone else. Another option is a reputable daycare, which is at least monitored so that if he is incessantly crying, you don't have to worry that he may not properly handled.
If you do not pay her, which surely would make it harder to simply change sitters, then I suggest you have a non-confrontational, heart-to-heart talk with her about what she is seeing from your son (in detail), and how she is responding, what your expectations are, and try to get on the same page about how to best care for your son. I would even go the extent as to draft up a plan of approach for your mother-in-law that outlines the steps she can take to emulate what you would do for your son if he is discontented or crying. A plan is always a good idea to help us address stressful situations. That way, you can skip ove the feeling of being overwhelmed in the moment trying to figure out what to do, and go straight to trying different solutions.
I would just approach it with her as your desire to help her in any way you can to make her time with your son more enjoyable and less stressful by getting on the same page about what he needs from her...
Hope this helps. Please feel free to contact me directly if you would like to chat more. :)