Simon, when there is a divorce, a court will usually require that the husband pay child support and often alimony. In the case of divorce, the children and Dijana would be receiving money from the same source they now receive it.
I think that is easier policed when someone has a more traditional defined role, where wages can be seen and deduced. Throw in "anonymous internet money" with "moved to a foreign country" and I think she may as well whistle dixie.