How can I match duplicated values in a column, examine the condition and output a final result in R?

Maybe something like this with tidy verse approach (tidyr::separate)

However it's a quick answer and I'm not sure to understand your data relations as you want.

library(tidyverse)

one <- tibble::tribble(
  ~ID, ~Position, ~Region,
  "a",    "1-50",   "D1a",
  "a",  "80-100",   "D2a",
  "a", "250-300",   "D3a",
  "b",  "50-100",   "D1b",
  "b", "150-180",   "D2b",
  "c",    "1-20",   "D1c",
  "c",   "50-80",   "D2c",
  "c", "100-200",   "D3c",
  "c", "250-300",   "D4c"
  )

two <- tibble::tribble(
         ~ID, ~Position,
         "a",       28L,
         "a",       85L,
         "a",      320L,
         "b",       55L,
         "b",      100L,
         "c",       18L,
         "c",       45L,
         "c",      180L,
         "c",      270L
         )


one_ <- one %>% 
  tidyr::separate(Position, c('p_min', 'p_max'), sep = "-") %>% 
  mutate_at(vars(starts_with('p_')), as.integer)

two %>% 
  mutate(rn = row_number()) %>% 
  left_join(one_) %>% 
  mutate(in_between = (Position >= p_min & Position <= p_max)) %>% 
  filter(in_between) %>% 
  distinct(rn, .keep_all = TRUE)

Joining, by = "ID"
# A tibble: 7 × 7
  ID    Position    rn p_min p_max Region in_between
  <chr>    <int> <int> <int> <int> <chr>  <lgl>     
1 a           28     1     1    50 D1a    TRUE      
2 a           85     2    80   100 D2a    TRUE      
3 b           55     4    50   100 D1b    TRUE      
4 b          100     5    50   100 D1b    TRUE      
5 c           18     6     1    20 D1c    TRUE      
6 c          180     8   100   200 D3c    TRUE      
7 c          270     9   250   300 D4c    TRUE