I transferred in no physics credits and only Calc 1. I had about 34 other transfer credits (each class being 4 credits. Almost all college, but some AP), but they were for humanities. As long as you have a decent background, you should have no problem with the transfer. If there are any deficiencies in the knowledge, either the professor or another resource would be help. I would transfer. With enough credits it gives flexibility in scheduling and the possibility to take a co-op or study abroad.
For the first two years, the path for CPEs and EEs is almost exactly the same. Electrical engineers take fundamental computer engineering classes and vice versa. At this point some of the EEs switch to become CPEs. If your DS is interested in Analog, then EE is definitely the way to go. There is one Computer Science class in the EE sequence along with some programming in the CPE classes. EEs also have to take power electronics and electrical and magnetic fields classes. There are analog specific classes as well. I’d suggest going on to the Rose Hulman course catalog and looking at the EE sequence and the course catalog of ECE classes to get an idea of some of the classes that would be taken.
Let me know if there is anything else you are curious about.