"In other words, it is postulated that a semi-independent relation links the nuclear family to the extended family. Because the extended family cannot offer a complete guarantee of occupational success it legitimates the moves of nuclear family members. On the other hand, receiving as it does significant aid in achieving many of its goals, the nuclear family retains its extended family connections despite geographical distance." (Litwak, Eugene. “Geographic Mobility and Extended Family Cohesion.” American Sociological Review, vol. 25, no. 3, 1960, pp. 385–394., www.jstor.org/stable/2092085.)
International Marriage is more than just the joining of two individuals from different nation-states, it also links two extended families in different countries and creates a web of kinship ties that transcend borders. This can be seen as an opportunity for all since immigration laws that favor family reunification make it possible for other family members to migrate, too. Remittances play a role as well with money being sent back to help family members in the home country. In Klekowski von Koppenfel's study of Americans in Europe, she found that American migrants sent money to family in the US to help pay for unexpected expenses like medical care.
There is opportunity but there are also obligations. Conflicts can and do arise when the couple must make decisions in favor of one extended family over the other. The couple (unless they are very wealthy) simply can not provide personal care to two sets of aging parents living in two different countries. And while there may be general agreement that some assistance is necessary there can be arguments over just how many resources the nuclear family can afford to transfer to one or the other's elderly parents.
Where to live, where to send the children to school, what languages to speak in the home are all issues that are salient to a bi-national couple and some are mutually exclusive or just very difficult to achieve. Caring for parents is one that is fraught with cultural expectations that neither spouse may be aware of until it becomes an issue. In some countries (US, UK) older people are encouraged (and want) to be independent. After a lifetime of caring for their children, they see retirement as freedom and don't want their children interfering in their lives. It is assumed by all that they will move into some sort of assisted living as they become less able to care for themselves.
Other countries and cultures have very different expectations. Parents remain active in their children's lives (and vice versa) and they help raise their grandchildren. A retirement home is a last resort - the ideal is to grow old at home with one's children and grandchildren. If the parents must be moved to a long-term care facility, it is still expected that the adult children play a large role in their parents' care. (Spain, Japan).
To complicate matters even further, different countries have different approaches to care for the elderly. Some countries like France or Sweden have state-provided services. France has something called allocation personnalisée d'autonomie (APA) which is a subsidy for people over 60. Sweden has similar subsidies and services. These things do not mean that family isn't involved in care, but it does mean that there are local resources to help the elderly whether they have family living nearby or not. In other countries like Japan the state has had less of a role (this is changing) and families still provide a lot of care.
These factors plus the distance or proximity of parents and limited financial resources make for some very hard decisions - decisions that involve both spouses and test their ability to be culturally aware and compromise. A foreign spouse may be surprised to learn that she is responsible for caring for the husband's parents while her parents rely on state care at home.. Another may be shocked to be told that the spouse's parents are moving with them because "that's what we do here." The native spouse may resent having to transfer money locally or abroad to help in-laws he or she hardly knows (or doesn't like very much). In the event of a crisis one spouse may need to purchase plane tickets and have to leave for extended periods. There may even be strong pressure to return "home" with an equally strong reaction on the part of the other spouse to stay. Gender certainly plays a part here since there may be more pressure on women to provide personal care, while men might feel more pressure to contribute financially.
Family connections are a social and biological fact, "family values" are not. The cultural context is extremely important and even very well-integrated migrants may discover that their assumptions about how parents should be cared for when they can no longer care for themselves differ dramatically from that of their spouse. Like other questions that require a projection into the future (where will we send the children to school?) most of us don't think about them until we must. And thinking of our parents as aging and needing care is one that most of us put off thinking about because we love them and want them to live forever. However, this is one we should probably discuss with our spouses beforehand. In my time here in Japan I have met migrants who married under very explicit terms - that they would take care of the spouse's parents in the host country first and that they would never leave Japan for long periods. That arrangement shows a foresight that many of us don't have.
I do wonder, however, about the fairness of such deals. Circumstances change. A decision made when one is 30 may not be the same one he/she would make at 50. For as our parents age, so do we. And when they are gone, we may be the ones needing care one day from our children who may be just as far from us as we were from our parents.