If you are going to drive down to UAE, you need to first go to the UAE embassy here and apply for the visa. Once you have the UAE visa, you may either drive to the border and get your Saudi Visa (not advisable for you as you are travelling with kids - sometimes the lines at the border could be REALLY long) Or you could go to the saudi embassy and just apply for it and make sure that you attach a copy of the UAE visa for faster processing.