dplyr的解（可能不是最短的解）：

# library
library(tidyverse)

# get data
df1 <- structure(list(id = c(12L, 123L, 10L), 
               day1 = c(2L, 0L, 3L), 
               day2 = c(1L, 3L, 3L), 
               day3 = c(2L, 0L, 3L), 
               day4 = c(1L,3L, 3L), 
               day5 = c(1L, 3L, 3L), 
               day6 = c(3L, 0L, 3L), 
               day7 = c(1L,3L, 3L), 
               Date = c("Monday", "Friday", "Saturday")),
               row.names = c(NA,-3L), class = c("data.table", "data.frame"))

df2 <- structure(list(id = c(12, 123, 10),
                      c1 = c(3, 3, 3), 
                      c2 = c(3, 2, 1),
                      Date = structure(c(3L, 1L, 2L), .Label = c("Friday", "Saturday","Wednesday"),
                                       class = "factor")), row.names = c(NA, -3L), class = "data.frame")

# change days to numeric (will help you later)
df1 %>% mutate(
  Date_nr_df1=case_when(
    Date=="Monday" ~ 1,
    Date=="Tuesday" ~2,
    Date=="Wednesday" ~3,
    Date=="Thursday" ~4,
    Date=="Friday" ~5,
    Date=="Saturday" ~6,
    Date=="Sunday" ~7)) -> df1

df2 %>% mutate(
  Date_nr_df2=case_when(
    Date=="Monday" ~ 1,
    Date=="Tuesday" ~2,
    Date=="Wednesday" ~3,
    Date=="Thursday" ~4,
    Date=="Friday" ~5,
    Date=="Saturday" ~6,
    Date=="Sunday" ~7)) -> df2

# combine data by the id column
left_join(df1,df2, by=c("id")) -> df     

# adjust data   
df %>%
  group_by(id) %>% # to make changes per row
  mutate(days=paste0(day1,day2,day3,day4,day5,day6,day7)) %>% #pastes the values together
  mutate(days_correct=substring(days,Date_nr_df1)) %>% # applies the start day
  mutate(Occurrence_seq=str_split(days_correct, fixed("0"))[[1]][1]) %>% # extracts all days before 0
  mutate(Occurrence=nchar(Occurrence_seq)) %>%  ## counts these days
  mutate(Occurrence=case_when(Occurrence==1 ~ 0, TRUE ~ as.numeric(Occurrence))) %>% # sets Occurrence to 0 if there is no consecutive occurrence
  mutate(Position=Date_nr_df2-Date_nr_df1+1) %>% ## calculates the position you wanted
  mutate(c1=case_when(Occurrence==0 ~0, TRUE ~ c1),
         c2=case_when(Occurrence==0 ~0, TRUE ~c1),
         Position=case_when(Occurrence==0 ~ 0, TRUE ~ as.numeric(Position))) %>% 
  ungroup() %>% ungroups the df
  select(id,c1,c2,Occurrence,Position) # selects the wanted variables
#> # A tibble: 3 x 5
#>      id    c1    c2 Occurrence Position
#>   <dbl> <dbl> <dbl>      <dbl>    <dbl>
#> 1    12     3     3          7        3
#> 2   123     0     0          0        0
#> 3    10     3     3          2        1

由reprex package（v0.2.1）于2020年4月10日创建