Going out to eat is not "working," at least for those who are doing the eating. And, you agree, apparently, that those who are doing the cooking and serving are not sinning, either, since they are so poor to begin with (they would not be working those jobs if that was not the case) that they, by necessity, can work on Sundays. So, I guess, what's the point of discussing this any further?
That was a ridiculous response. Just because a person work in a restaurant does not imply that he is poor or that he actually have to be working on a Sunday. Stop making presumptions.
A person who fears God and cares for his salvation is obliged to look for another work where he is not forced to work on a Sunday. If he can do it (change work), but refuse, he commits a mortal sin.
Eating out is not a work no. But that does not change the fact that you in fact are helping a person in a possible mortal sin of unnecessary work on Sundays. Since we cannot know who is working on necessity, we cannot presume, that you do, that all people working on a Sunday has necessity.
It's a certain fact, that most people working on Sundays has no necessity for doing so. In the richer countries, wages are high, and many people today live like kings compared to poorer countries. Many people could stay away from work on Sundays, or change their work, but simply refuse to do so. This is a clear mortal sin.
If you have exhausted all the options for receiving an income, for ex: looking for another job or moving to another place, or any other lawful means of receiving an income, (like receiving social welfare checks for the support of the necessities for you or your family, as long as this do not imply that you have to compromise your faith in any way,) then you are not obligated to stay away from work and can safely work on Sundays as long as it is your last option. Below are some examples of acceptable reasons of why you can work on Sundays.
If you cannot continue home-schooling your children for example, this would be an acceptable reason with continuing to work on Sundays, another example would be if you had to move to a bad neighborhood with much drugs, violence or lasciviousness that would influence you or your family in a sinful way, or if by quitting your work, you may be forced to take another work that is sinful or immoral. This would be another reason to continue to work on Sundays until you have found another work where you are not forced to work on Sundays or forced to put your family's spiritual wellbeing in jeopardy.
This goes to say if the work you do is acceptable before God. If you sin against God by the specific work you do, such as selling contraception, porn, bad newspapers with immodest images or stories about sex or other sins etc, then you cannot go to that work even if you starve or don't have the means to support yourself or your family. In such cases you have to put your entire trust in God. You cannot be the cause of your brothers mortal sins without yourself being guilty of mortal sin!
“Therefore I say to you: Be not solicitous for your life, what you shall eat, nor for your body, what you shall put on. The life is more than the meat: and the body is more than the raiment... seek ye first the kingdom of God and his justice: and all these things shall be added unto you.” (Lk. 12:22-24, 27-28, 31)
However, in the poorer countries where there is no chance of getting social welfare or income in any other way, it is totally acceptable to work on Sundays as long as the person must do it in order to survive. Many people do not operate under these conditions but work on Sundays in order to have more money than they need to survive. Yes, many people have the means necessary to stay away from work on Sundays, but only go to work to receive more abundance in riches. This is a clear mortal sin!