Navion,
You will love the Rose Parade. As Seilerbird suggests it is fun to see the floats up close and personal on the day after the parade if it fits into your schedule.
When you travel from San Diego on Interstate 8, you will indeed come very close to the border with Mexico. In fact when you pass through the Imperial Sand dune area you can actually see the Border FENCE . But the area is safe . Just watch for tourist traffic in the area.
I would guess from San Diego to your connection at Interstate 10 you will pass through at least 2 Border Patrol checkpoints. One is in the mountain pass area in California, the other is outside of Yuma before you get to Gila Bend. They will ask if you are US citizens, where you are heading and tell you to have a nice day. All this chit chat is going on while their highly trained dogs are sniffing your rig for drugs. It seems RV's have been a vehicle of choice for many smugglers so we all get the look see. It's ok with me.
Do consider the third week in January for a stopover in Quartzsite. It is a social phenomena unlike any I've ever seen, where tens of thousands of RV's converge on a desolate area of the desert.