The charity urged governments to clearly set out guidelines for families whose parents live apart.
A charity supporting separated families has recorded an 81% increase in enquiries during the lockdown.
Shared Parenting Scotland (SPS) said 991 people got in touch via phone, email or text between 1 March and 31 May to seek advice about arrangements for children whose parents live apart.
Some parents who have contacted the charity say their former partners have refused to share in the care of their children during lockdown, while others expressed concern over potential health implications of children moving between two households.
The charity also received a number of calls about the legal aspects of children crossing the border between Scotland and England to visit a parent following the divergence of lockdown rules between the two countries.
SPS said that in many cases the enquiries show some parents are exploiting the regulations for their own benefit, and urged both the UK and Scottish Governments to use their daily briefings to clearly set out the guidelines on shared parenting.
Ian Maxwell, SPS national manager, said: ''It was set out in the lockdown law from day one that travel for children under the age of 18 to continue contact arrangements with parents who do not live together is an exception to the overall travel restrictions. The legal guidance from the lord president in Scotland and the president of the family division in England and Wales was that court orders should be complied with.
“Many of the calls we have received have simply sought clarification or reassurance. Some parents have genuinely stepped up and made arrangements that make sense for both parents and their children. Unfortunately, others have not. We have been contacted by many parents who say that not only contact but all communication has stopped.
“There's no doubt that the effect of the daily recitation of death and illness statistics has been to induce a fear about leaving home that can't just be switched off. It is also clear from our calls that some parents have exploited the lockdown to disrupt the relationship between their children and a separated parent. We urge all parents to put the wellbeing and emotional health of their children at the top of their priorities.''
