I am not sure to understand all what you want to do since you don't provide the expected result. Here a solution using IRanges
package. It is maybe not simple to understand at first reading but it is extremely useful to find overlaps for continuous intervals.
library(IRanges)
## create a time intervals
subject <- IRanges(as.numeric(emtek_file$entry_emtek),
as.numeric(emtek_file$exit_emtek))
## create a time intervals (start=end here)
query <- IRanges(as.numeric(hidenic_file$hidenic_time),
as.numeric(hidenic_file$hidenic_time))
## find overlaps and extract rows (both time point and intervals)
emt.ids <- subjectHits(findOverlaps(query,subject))
hid.ids <- queryHits(findOverlaps(query,subject))
cbind(hidenic_file[hid.ids,],emtek_file[emt.ids,])
hidenic_id hidenic_time emtek_id entry_emtek exit_emtek
8 110387 2001-03-13 22:29:56 3 2001-03-13 22:29:56 2001-03-14 22:29:56
9 110388 2001-03-14 01:03:30 3 2001-03-13 22:29:56 2001-03-14 22:29:56
41 110420 2001-06-09 16:56:26 7 2001-06-09 16:56:26 2001-06-10 16:56:26
Ps: to install the package :
source("http://bioconductor.org/biocLite.R")
biocLite("IRanges")