The reversed Three of Wands indicates that your family may not agree with your ideals. This means that it is important to learn to listen to the opinions of others before making your own judgments. It could also mean that in your family there is difficulty finding common ground on which to discuss and reach a point of agreement. This would require all family members to exercise some patience and mutual respect.
The World indicates that while your family may not always agree with your ideals, they are all aware of the importance of collaboration and the need to find compromises to achieve a common goal. This suggests that your family is strong enough to accept that people can have different points of view on a given topic without getting into heated arguments with each other. This also means that your family has a strong sense of responsibility and knows how to deal with difficult situations.
In conclusion, we can say that your family's strengths are mutual respect, collaboration and the ability to be satisfied while maintaining their ideals. These qualities make them strong and supportive, thus making them ready to face any challenge together.