Is it permissible for a woman to travel to her husband residing abroad, given the presence of her elderly and sick parents in her home country, and would this be considered disobedience, bearing in mind that she does not serve them but only visits them?

It is obligatory for children to care for their elderly parents equally, each according to their circumstances. If the daughter is the only one living with her parents, she must care for them to the best of her ability. However, if they are able to manage their own affairs and do not require her care, then there is no blame upon her for traveling to her husband.