My DS never went to daycare, he did go to pre K when he was 4. DTAP was the only vax he was fully current on (he only had one of Hib.) I did it b/c I could imagine him getting a puncture wound on a playground or whatever and being worried to death about tetanus, which though rare in the US does have a fairly high fatality rate (? 50%)
The only other VPD that concerns me enough to get a vax for at this point is meningitis, but it is not recommended for young children (yet.) The other childhood diseases (chicken pox, mumps, measles) aren't typically deadly and it is preferable to get them in childhood & get natural immunity IMO. At the time I was making vax decision for my DS, they were considering removing polio from the schedule since it is not in the US anymore so I didn't do it. Since then, there have been outbreaks in some places in Africa where people had stopped vaxing. I believe there has also been outbreaks in Afghanistan. Still I think it extremely unlikely it will come back to the US.
Rotavirus causes diarrhea, which if you are not living in a 3rd world country should be easy to treat. The vaccine is contaminated with DNA from a pig virus ( wasting piglet disease?) which doesn't concern the CDC apparently but after reading about the SV40 virus from the oral polio vax being found in human cancer tumors I wouldn't take a chance on it.
Are you worried about any disease in particular? If you don't want to be hassled about it by your father, have you tried just redirecting him when he brings up the subject? IE, "Dad, I know you are concerned and I hear what you are saying but you aren't going to change my mind so I'm not going to discuss it with you." OR you could always just lie and tell him what he wants to hear