Generally, a parent can structure his or her time during visitation with a child (or during primary parenting time, if the parent is the primary residential parent), without much input from the other parent.
Restrictions often exist relating to taking a child outside the country without prior permission, but generally, in other respects, the parent who has time with the child can determine what that parent and the child do during this parenting time.
In some cases, there are pre-existing agreements allowing for international travel, or a particular trip that has been preapproved by both parents.
In the rapidly evolving world of travel we now face, with the Coronavirus/COVID 19 Pandemic, sticking to such plans may not be a good idea.
Travelers in many countries are now effectively stuck in those countries, since there are countries which have severely limited internal travel, and which have completely cut off international travel, not only into those countries, but also leaving those countries.
Even travel within the US may become difficult, as domestic travel restrictions are considered.
Being trapped in even the nicest vacation spot can become a nightmare, and a nightmare that only gets worse if the travel restrictions go on for two or more weeks, as is becoming increasingly common.
Being trapped away from home can also be an increasingly difficult situation when hotels and restaurants are shut.
Extending a holiday (while being trapped in a single room) can also become very expensive, if you are paying resort hotel and restaurant prices.
Hotels and restaurants have been closed by government order in several countries already.
Many airlines have severely restricted their flight schedule, even where governments are still allowing flights in and out of a country or region. Some countries have also severely limited train transport, and have shut down long distance trains.
Traveling by cruise ship or ocean liner has become increasingly fraught, as some ships have been refused docking privileges for extended periods, and have been shuttled from port to port. Other ships have been allowed to dock, but the passengers have been trapped on board for very extended periods.
Many major hotels in the US are shutting down, due to a lack of business, and are turning away people who had pre-existing reservations. This can also develop into an extremely difficult situation if you are trapped away from home.
Even if a parent has the right to determine what happens during his or her pre-scheduled visitation or parenting time, insisting on exercising that right may be unwise, and may not be in the best interests of a child.
Careful thought should be exercised in this new situation we face.
There is, of course, risk in life, inherently. I was taken to places with riots, incipient civil wars, cholera, and the like as a child. But the risks were carefully weighed, and determinations of what to do, when, and whether to not do certain things after all were all carefully reviewed and decided on in concert. Be careful, think carefully, and put the best interests of your children first when deciding whether to follow through on plans you may have made in the past - and if there is disagreement between the parents in a situation where there is a parenting plan, think carefully about whether standing on your rights and following through with prior plans is in the best interests of the children - and whether a court will agree that your actions were in the best interests of the children when they review the situation in hind sight, if the other parent claims later that you did not act in the best interests of your children.