Vicki Pallister's children
Vicki Pallister and Troilus had two children in the 12th century BC. Vicki called them both "little heroes". (AUDIO: Frostfire)
When the TARDIS reappeared in an olive grove in Carthage, Vicki told her grandson Antiphus to tell his father that she loves him. (AUDIO: Fugitive of the Daleks)
Alternate timeline
In an alternate timeline, Vicki had two daughters named Carla and Maria with her husband, Jeran Dalton, on Astra. When the timeline was further altered, she had a son named Carl instead of Carla. The timeline was eventually undone but Vicki retained the memories of her family and chose to preserve them. (AUDIO: The Crash of the UK-201)
Behind the scenes
In The Storyteller, a minisode released in conjunction with the announcement of Doctor Who: The Collection — Season 2 Blu-ray boxset, Vicki is seen talking to a young child, Sophia, and mention is made of Sophia's mother. While it is implied that they are related to Vicki, it is not explicit.