@jackstack If the grandmother is happy with it and you're confident she could handle any early waking or nighttime issues, I don't see why your son can't spend the night there.
Having said that, three times a month is quite a lot of sleepovers. This is doubly true if your mother-in-law is already having him during the day four times a week. It's a significant committment in terms of both time and energy, so you may want to check if your wife is hesitant because she's worried your son would struggle with being away, or whether her mum would struggle with the extra childcare.
Or, I suppose, a combination of both.
For what it's worth, I know my folks would love to have my son stay in theory, but they would be either cranky or exhausted by the end of week two. However, my wife's cousin used to have her sons stay with their grandma every Friday night and it seemed to work well for them.