Вы можете построить интересующие и подмножества диапазонов:
library(lubridate)
date <- seq(as.Date("2001-07-20",origin="1970-01-01"),as.Date("2010-12-31",origin="1970-01-01"),by = 1)
range1 <- as.Date(unlist(lapply(c(0:4),function(y) seq(as.Date("2004-06-23",origin="1970-01-01"),as.Date("2004-07-13",origin="1970-01-01"),by="1 day") + years(y))),origin="1970-01-01")
range2 <- as.Date(unlist(lapply(c(0:4),function(y) seq(as.Date("2004-07-20",origin="1970-01-01"),as.Date("2004-08-09",origin="1970-01-01"),by="1 day") + years(y))),origin="1970-01-01")
date[date %in% range1 | date %in% range2]
Альтернатива
Альтернативный ответ, используя% между%, как предложено в OP
library(lubridate)
dates <- seq(as.Date("2001-07-20"),as.Date("2010-12-31"),by = 1)
r1 <- c(as.Date("2004-06-23"),as.Date("2004-07-13"))
r2 <- c(as.Date("2004-07-20"),as.Date("2004-08-09"))
ranges <- lapply(c(0:4),function(y) list(r1=r1 + years(y),r2=r2+years(y)))
as.Date(unlist(lapply(ranges,function(r) { dates[dates %between% r$r1 | dates %between% r$r2] })))