R: Update/generate variables without loop - r

Question

How can I generate or update variables without using a loop? mutate doesn't work here (at least I don't know how to get it to work for this problem) because I need to calculate stuff from multiple rows in another data set.
I'm supposed to replicate the regression results of an academic paper, and I'm trying to generate some variables required in the regression. The following is what I need.
I have 2 relevant data sets for this question, subset (containing
geocoded residential property transactions) and sch_relocs (containing the date
of school relocation events as well as their locations)
I need to calculate the distance between each residential property and the nearest (relocated) school
If the closest school is one that relocated to the area near the residential property, the dummy variable new should be 1 (if the school relocated away from the area, then new should be 0)
If the relocated school moved only a small distance, and a house is within the overlapping portion of the respective 2km radii around the school locations, the dummy variable overlap should be 1, otherwise 0
If the distance to the nearest school is <= 2km, the dummy variable in_zone should be 1. If the distance is between 2km and 4km, these transactions are considered controls, and hence in_zone should be 0. If the distance is greater than 4km, I should drop the observations from the data
I have tried to do this using a for loop, but it's taking ages to run (it's still not done running after one night), so I need a better way to do it. Here's my code (very messy, I think the above explanation is a lot easier if you want to figure out what I'm trying to do.
for (i in 1:as.integer(tally(subset))) {
# dist to new sch locations
for (j in 1:as.integer(tally(sch_relocs))) {
dist = distHaversine(c(subset[i,]$longitude, subset[i,]$latitude),
c(sch_relocs[j,]$new_lon, sch_relocs[j,]$new_lat)) / 1000
if (dist < subset[i,]$min_dist_new) {
subset[i,]$min_dist_new = dist
subset[i,]$closest_new_sch = sch_relocs[j,]$school_name
subset[i,]$date_new_loc = sch_relocs[j,]$date_reloc
}
}
# dist to old sch locations
for (j in 1:as.integer(tally(sch_relocs))) {
dist = distHaversine(c(subset[i,]$longitude, subset[i,]$latitude),
c(sch_relocs[j,]$old_lon, sch_relocs[j,]$old_lat)) / 1000
if (dist < subset[i,]$min_dist_old) {
subset[i,]$min_dist_old = dist
subset[i,]$closest_old_sch = sch_relocs[j,]$school_name
subset[i,]$date_old_loc = sch_relocs[j,]$date_reloc
}
}
# generate dummy "new"
if (subset[i,]$min_dist_new < subset[i,]$min_dist_old) {
subset[i,]$new = 1
subset[i,]$date_move = subset[i,]$date_new_loc
}
else if (subset[i,]$min_dist_new >= subset[i,]$min_dist_old) {
subset[i,]$date_move = subset[i,]$date_old_loc
}
# find overlaps
if (subset[i,]$closest_old_sch == subset[i,]$closest_new_sch &
subset[i,]$min_dist_old <= 2 &
subset[i,]$min_dist_new <= 2) {
subset[i,]$overlap = 1
}
# find min dist
subset[i,]$min_dist = min(subset[i,]$min_dist_old, subset[i,]$min_dist_new)
# zoning
if (subset[i,]$min_dist <= 2) {
subset[i,]$in_zone = 1
}
else if (subset[i,]$min_dist <= 4) {
subset[i,]$in_zone = 0
}
else {
subset[i,]$in_zone = 2
}
}
Here's how the data sets look like (just the relevant variables)
subset data set with desired result (first 2 rows):
sch_relocs data set (full with only relevant columns)