There are no hard and fast answers to your questions about traffic and drive times, of course, but some typical numbers would be that the drive from Alpine to a site in central San Diego would take 30-45 minutes in 'typical' traffic depending on your exact destination. San Diego also has pretty typical rush hour time, say 4:00 to 6:00, but I'd suggest you try to avoid driving between 3:00 and 7:00 in the afternoon/evening if you're not familiar with the roads.
As for Saguaro National Park/Desert Museum, I would highly recommend the Arizona-Sonora Desert Museum. Although it can be a bit pricey for an entire family, you will learn more about the desert and its creatures there than you will in the national park. Try to time your visit to coincide with one of their major demonstrations. I particularly recommend the Raptor Display, but even if there is no major demo, there will be docents situated around the park with smaller opportunities to meet some desert critters up close and personal. You pretty much have to drive through the park to get to the museum, so you'll definitely see the cacti. You should also try to get to the museum by taking Speedway Boulevard west out of Tucson over Gates Pass and then follow the signs. The electric streetcars are not currently running as their route is undergoing a major expansion and the tracks are torn up, and will be for some time to come.