Petunia Dursley pretended she had no sister. It was not out of spite or jealousy (well a little was jealously) but for protection. Her sister Lily had a secret that was so dangerous, Lily's family had to go in hidding and Petunia had to pretend Lily did not exist. It was not a simple secret like she was a witch and went to a magic school. It was not even that she came from a muggle (non magical family). No it was because her precious son Harry was involved in a terrible prophesy with a terrible monster named Voldemort.
This Dark Lord had gained power 3 years ago and was causing havoc not only in magical world but non magic one too. when Lily found out that this dark lord was targeting non magical families she explained in great detail to her family what that meant. Their parent's remembered the atrocities of Holocausts. They had family and friends that survived and some that did not. Contingency plans were developed such as hidden rooms, alarm systems, false entries all muggle of cause. Lily researched magical protections and found that amulets were safest for family and runes to alert for intruders. Any other protection needed government approval which could easily be corrupted.
When their parents died in a car accident, both sisters were engaged. They had a meeting before Petunia was married to discuss their plans. Voldemort was getting stronger and was targeting smart muggle borns and trying to lure purebloods to their cause. As that included Lily and her fiance James it was getting too dangerous to be associated. They discussed ways to pretend their relationship was over and decided at Petunia's wedding where she will disown Lily and then sent a letter sauing she is not going to Lily's wedding.
It was also agreed to havw a secret code if there was an emergency.
The plan went perfectly and all went well untill the Potters (Lily and James) were told of a prophesy.