Collared dove fledgling advice

Hi, 

I have two in a low branch in my back garden easily accessible by my expert hunter of a cat Barney. 

I have been keeping her in for nearly a week until they fledged then yesterday they both flew away. I was therefore surprised to see them both return to the nest last night. This morning they were both there with a parent. This afternoon they still remain. 

I am nervous to let the cat out. Is this normal behaviour for collared doves? I’ve tried to find info about the behaviour of fledglings but couldn’t. Any idea how long it will be until I can let my cat out / they will fly away as she is determined to be outside and I worry she will get them. I will be sad to see them leave but it’d be worse if my cat got to them.