Shiri Bibas and her children, four-year-old Ariel and 10-month-old Kfir are yet to be released and there has been no word of them.
Their family has been told they might have been passed on by Hamas to another group in Gaza.
Speaking to Sky News, Shiri’s cousin Yifat said the wait is agonising.
She said: “What are these groups? We reach a dead end every time we try to figure out why Hamas is having so much trouble getting them back or whether that means if they’re alive or not.
“It’s really frustrating. It feels very far away, although it’s really close by. Hamas is ruling over the strip, and I hope that whichever group is holding them will oblige and will give them [back]. They said that they’re going to move those hostages into Hamas hands, so I hope those groups will do that as well.”
If Shiri Bibas and her children have been passed on to another group, it will explain why they haven’t been released and complications.
“I think they’re playing games with the psychological games,” said Yifat.
“It’s brutal. But what can you expect from a terror organisation that did such horrendous things? It’s amazing that a baby became some sort of a card or, you know, a winning card or a trophy holding him hostage like this to get more arms or, I don’t know, fuel for their missile launchers.”
The extension to the truce is due to end late on Wednesday night. Intense talks are going on behind the scenes to extend it further and public statements by both sides suggest that might be possible.
Yifat says she would support an extension in the ceasefire if it resulted in more hostages being released.
She said: “Every last one, all 240, everyone should be back home with their families. We are only one story.
“There’s a lot of mothers, a lot of children waiting for their parents that are being held captive. Every family of someone who was abducted, lost someone, lost their grandparents, and they don’t know it yet.
“I can’t stop thinking about Kfir, what he is eating, is he bathing, is he hitting his milestones?
“You see those children coming back and hearing the stories about how they didn’t eat anything. Almost nothing. He needs his baby formula, he needs his nutritions. Every day counts in this matter. Every day counts.
“You know, if we wait another day, maybe we will lose him.”