As much as you dont want to hear this, your parents are wrong in discussing this with the rest of the family. Probably lots of lashon hara and rechilus and possibly some motsi shem ra for good measure going around the house right now. The only one who must agree with the decision of your brother in law, is your sister. Can we assume he make the decision in consultation with his Rebbe or Rav?
You should stay out of it. When your parents discuss this walk away, you are not obligated to listen. If your parents keep this up, your sister and brother in law will stop visiting altogether and will probably break off contact. Do your parents want that?
As for your shidduch, if your parents keep badmouthing your sister and brother in law it will eventually get around. the other side will probably start to say things about your parents. Then 3rd parties will get involved (to defend the honor of their chashuve friends). Word will get around, do you think anyone would want to touch your family with a ten foot pole?
Your parents have a right to disagree with his decision to go to work. As adults, they might want to try having a rational discussion with their daughter and son in law to understand what is behind his decision. They dont have to agree with it, just respect the fact that he made a decision that they disagree with.
There is surely more going on than just this.