Can particle と and で both mean with?

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Why is particle で used instead of particle と in 家族で出かける (Kazoku de dekakeru)?

For example:

1. 
   

   今晩家族でレストランに行きます。(Konban kazoku de resutoran ni ikimasu) Tonight, I will go to the restaurant with my family.

   
   


2. 
   

   私は来週父と京都に行きます。(Watashi wa raishuu chichi to Kyouto ni ikimasu) I will go to Kyoto with my father next week.

   
   

Does it matter which I use? I think と is more common for saying "with someone" right? Just curious, thanks.

Also, is there a different connotation or feeling given if you use one over the other?