Is it permissible to exchange an abaya received in a dawah camp for another for a temporary period due to travel, and is there any blame upon her for doing so after she was told that it would be a proof against her?

There is no harm in wearing the desired abaya and leaving the other if it fulfills the conditions of the Sharia-compliant dress. No specific type of clothing is stipulated for women; rather, what is required is that the conditions be met. The camp supervisor intends adherence to the Sharia-compliant hijab, not an obligation to wear a specific abaya.