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The Precepts of the Catholic Church say:
You shall attend Mass on Sundays and on holy days of obligation and rest from servile labor
There are already several discussions about what servile labor is, boiling down to things that are more work than recreation (I'm simplifying here).
Is it also unlawful to cause others to perform servile work? Examples might be eating out or shopping on Sunday.
At least as regards some of the activities mentioned in the O.P.—especially, eating out—it is not problematic for those who are dedicated to providing others with leisure to do so on Sunday or other holy days.
The Catechism of the Catholic Church states expressly:
Sanctifying Sundays and holy days requires a common effort. Every Christian should avoid making unnecessary demands on others that would hinder them from observing the Lord’s Day. Traditional activities (sport, restaurants, etc.), and social necessities (public services, etc.), require some people to work on Sundays, but everyone should still take care to set aside sufficient time for leisure (no. 2187, emphasis added).
Regarding keeping stores open, the situation is less clear. Some stores are clearly a public service (pharmacies, etc.), and so keeping them open is not a problem. In other cases, whether there is truly a need to keep the stores open is a matter for prudential judgment, and so the Church has refrained from making any detailed pronouncements.
In any event, in societies (such as the United States) that are predominantly non-Catholic, it is simply not prudent or possible to control when stores will be open. Catholics are not expected to refuse to work on Sunday and holy days, especially if their future employment or advancement is placed in jeopardy. (It would, however, certainly be a good gesture on an employer’s part to allow Christians to take Sunday off, to the degree that it is possible.)
It follows, then, that there is no absolute prohibition against causing others to work on Sunday. An effort should be made to help others keep their Sunday rest to the extent possible, and so it seems prudent to refrain from unnecessarily requiring others to work—e.g., by doing the weekly grocery shopping on a Sunday. This is, however, a prudential judgment, not a question of a strict moral prohibition.
(My answer to the O.P.’s related question, According to Catholicism, is going to work on Holy Days of Obligation sinful?, will also shed light on this question.)
Regarding giving others an occasion to sin, St. Thomas Aquinas gives a similar scenario when explaining that one can without sin borrow from someone who exacts usury.
St. Thomas writes (Summa Theologica II-II q. 78 a. 4 arg. 2) that
for no temporal advantage ought one to give another an occasion of committing a sin: for this pertains to active scandal, which is always sinful, as stated above (q. 43, a. 2).
Thus, if you go to a restaurant on a holy day with the intention of making those working there not observe the holy day, then it is a sin.
