Unfortunately, this is a story that I hear often, and experienced. My first Sous Chef job was at $22,000 and once I figured out my hourly pay, taking into account time and half for OT, I was making less than my last cook gig. First off, once you go salary never do the math to figure out your hourly-it's too painful. I understand the bosses desire to cut labor by cutting the hourly staff, but I think there needs to be some give and take. Sure there are days when you just need to cut and close up by yourself, but there are times when things need to get done, extra cleaning needs to happen. Just make sure that your team is staying busy. It's hard, as an Exec. Chef or GM, to believe that you really need those guys, if I walk through the kitchen and see a bunch of them standing around, going out for their 5th cigarette, making a snack, harassing the waitstaff, etc.
You need to accept though, that if you want to stay salaried, your work weeks are going to average 50+ hours a week, often more. When I was in the restaurant world it wasn't unusual for me to work 70+ hour weeks or more. It's getting better in the industry, but the expectation is still working lots and lots of hours. I remember when I first left the restaurants and went into institutional food, I used to feel guilty after only putting in 40-45 hours.
It never hurts to ask for a raise, but if your bosses were like many of mine the standard response was that you knew what salary you were being offered and you knew what kind of hours you would be working so unless you can show them real cost savings since you've come onboard, they probably won't give you much of a raise, if any.
On the bright side you don't have $60k in student loan debt.
Cheer up a bit, your salary will increase. If the restaurant does well, if you find efficient ways to do things, if you schedule better, you might even get to sleep in, get 3 days off every two weeks.
Of course not all of them will happen all at once.
I didn't know this movie was still playing. This is one of those deal that they walk up to you pat you on the back and give you a position. Then after all the celebration is over reality sets in. Watch out what you wish for! If you plan on being a line cook all your life then go back to working the line. I would work as a Sous for a year and then either try for a chef position or a better paying Sous position at another restaurant. This isn't an easy profession to be in with a family. Make the best of the family situation and work toward a better paying position in the near future. You may not be making a lot now but, try to think of whats down the line.......
To my mind, albiet not knowing cost of living out there, you're massively underpaid. Get the money you need to make it worth the hours or walk. Talk is cheap; it literally costs your boss nothing. My personal philosophy is to ask for, and get, what I want when I take a job. Raises in this business are few and far between.
Edit: I know what's expected when I take a job. You didn't and it doesn't sound like you were 'offerred ' the job, but rather gifted it. I personally feel that that is incredibly unethical.
IMHO, Grande is right on the money. You can only be salary if your work meets certain conditions. Otherwise you are being taken advantage of. With a wife and three children, start looking for a job with better pay and hours. Institutional cooking may be the way to go, depending on your area. But you are currently being taken advantage of.
I have had some similar experiences over the course of my career and in my case the offers of change in money or working condition always came too late, as in after I gave notice. Owners that will take advantage of you, will not change until forced to and bottom line is why in the world would I want to stay in those situations?
The last time it happened, I was sous and fed up with the whole scenario. I actually had an opportunity to open my own restaurant, so I gladly gave my notice. The owners actually told me that if I would stay, changes would be made, also I would get more money, and I would be promoted to chef and the present chef would be moved down to become my sous. I don't know what was more hilarious, the fact that their son was the present chef, or the fact that they thought I would stay instead of going and opening my own place.
Every time something similar has happened, and this place was no different, the businesses wound up closing probably six months or so after I left; not because I am so great and the glue that held them together; but because they were owners without a clue or concern about me other than how much could they get for how little. Like I said, why in the world would I want to stay?
There's a thousand restaurants where you could go and make $7/hour (once you divide your salary by hours worked). Run, don't walk. They're screwing you big time. Unless you sorely need the experience and the title on a resume this is gonna be a soul sucking waste of your time. At a minimum tell them you will only work there for an hourly wage. It's understood that salary = slavery, but it can have some upsides if the pay is tolerable (eg. stable paychecks, never worrying about your hours getting cut, etc).
You have to CYA, they're looking out for themselves so you have to look out for yourself.