Not generally, part of the natural process for the mother of our pets is to chase off the young so she can prepare for a new litter. The youngsters may miss her at first but they soon adapt and forget about the family, this is why if you keep the males and females together (even closely related) they will mate because they don’t know they are related.
Having said that any animals kept as pets can bond together and pine or miss each other if one goes, but that is not because they are related.
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