require(tidyverse)

unite2 = function(x, col, ..., sep = '_', remove = TRUE){
  unite(x, 'tmpcol', ...,  sep = '∞-∞', remove = remove) %>%
    mutate(tmpcol = tmpcol %>% str_remove_all('∞-∞NA(?=∞|$)') %>% str_replace_all('∞-∞', sep)) %>%
    rename(!!col := tmpcol)
}

x = tibble(x=c('the','a','my'), y=c('brown','cat',NA),z=c('dog',NA,'bird'))
unite2(x, col = 'xzy', c('x','y','z'), sep=' ')
#> # A tibble: 3 x 1
#>   xzy
#>   <chr>
#> 1 the brown dog
#> 2 a cat
#> 3 my bird