Using rvest to login into webpage with pop up sign in - r

Question

I would like to login to a webpage with a pop up sign in window. This article logs into Stack Overflow, a webpage that has a visible login form. How can I use rvest to login into websites that don't have visible login forms? For example, the Washington Post's website has a sign in box on the top right of the page. Once clicked, a form appears where you can sign in.
library(rvest)
url <- 'https://www.rotary.org/myrotary/en'
url2 <- 'https://stackoverflow.com/users/login?ssrc=head&returnurl=http%3a%2f%2fstackoverflow.com%2f'
url3 <- 'https://www.washingtonpost.com/?noredirect=on'
If I get the structure of the forms on StackOverflow's login page,
pg_session <- html_session(url2)
html_form(pg_session) %>% str
List of 2
$ :List of 5
..$ name : chr "search"
..$ method : chr "GET"
..$ url : chr "/search"
..$ enctype: chr "form"
..$ fields :List of 2
.. ..$ q :List of 7
.. .. ..$ name : chr "q"
.. .. ..$ type : chr "text"
.. .. ..$ value : chr ""
.. .. ..$ checked : NULL
.. .. ..$ disabled: NULL
.. .. ..$ readonly: NULL
.. .. ..$ required: logi FALSE
.. .. ..- attr(*, "class")= chr "input"
.. ..$ <unnamed>:List of 7
.. .. ..$ name : chr "<unnamed>"
.. .. ..$ type : chr "submit"
.. .. ..$ value : NULL
.. .. ..$ checked : NULL
.. .. ..$ disabled: NULL
.. .. ..$ readonly: NULL
.. .. ..$ required: logi FALSE
.. .. ..- attr(*, "class")= chr "button"
.. ..- attr(*, "class")= chr "fields"
..- attr(*, "class")= chr "form"
$ :List of 5
..$ name : chr "login-form"
..$ method : chr "POST"
..$ url : chr "/users/login?ssrc=head&returnurl=http%3a%2f%2fstackoverflow.com%2f"
..$ enctype: chr "form"
..$ fields :List of 7
.. ..$ fkey :List of 7
.. .. ..$ name : chr "fkey"
.. .. ..$ type : chr "hidden"
.. .. ..$ value : chr "d5f8c65b7d92b368b4b58e43e59fd9d82cb4436bac4a6d430771d50b85e771aa"
.. .. ..$ checked : NULL
.. .. ..$ disabled: NULL
.. .. ..$ readonly: NULL
.. .. ..$ required: logi FALSE
.. .. ..- attr(*, "class")= chr "input"
.. ..$ ssrc :List of 7
.. .. ..$ name : chr "ssrc"
.. .. ..$ type : chr "hidden"
.. .. ..$ value : chr "head"
.. .. ..$ checked : NULL
.. .. ..$ disabled: NULL
.. .. ..$ readonly: NULL
.. .. ..$ required: logi FALSE
.. .. ..- attr(*, "class")= chr "input"
.. ..$ email :List of 7
.. .. ..$ name : chr "email"
.. .. ..$ type : chr "email"
.. .. ..$ value : NULL
.. .. ..$ checked : NULL
.. .. ..$ disabled: NULL
.. .. ..$ readonly: NULL
.. .. ..$ required: logi FALSE
.. .. ..- attr(*, "class")= chr "input"
.. ..$ password :List of 7
.. .. ..$ name : chr "password"
.. .. ..$ type : chr "password"
.. .. ..$ value : NULL
.. .. ..$ checked : NULL
.. .. ..$ disabled: NULL
.. .. ..$ readonly: NULL
.. .. ..$ required: logi FALSE
.. .. ..- attr(*, "class")= chr "input"
.. ..$ submit-button:List of 7
.. .. ..$ name : chr "submit-button"
.. .. ..$ type : NULL
.. .. ..$ value : NULL
.. .. ..$ checked : NULL
.. .. ..$ disabled: NULL
.. .. ..$ readonly: NULL
.. .. ..$ required: logi FALSE
.. .. ..- attr(*, "class")= chr "button"
.. ..$ oauth_version:List of 7
.. .. ..$ name : chr "oauth_version"
.. .. ..$ type : chr "hidden"
.. .. ..$ value : NULL
.. .. ..$ checked : NULL
.. .. ..$ disabled: NULL
.. .. ..$ readonly: NULL
.. .. ..$ required: logi FALSE
.. .. ..- attr(*, "class")= chr "input"
.. ..$ oauth_server :List of 7
.. .. ..$ name : chr "oauth_server"
.. .. ..$ type : chr "hidden"
.. .. ..$ value : NULL
.. .. ..$ checked : NULL
.. .. ..$ disabled: NULL
.. .. ..$ readonly: NULL
.. .. ..$ required: logi FALSE
.. .. ..- attr(*, "class")= chr "input"
.. ..- attr(*, "class")= chr "fields"
..- attr(*, "class")= chr "form"
, I can clearly locate where to fill out my email and password. However, I can't find it in the structure of the forms on the Washington Post's home page, which makes it difficult to call the form I need.
pg_session <- html_session(url3)
html_form(pg_session) %>% str
List of 1
$ :List of 5
..$ name : chr "search-form"
..$ method : chr "GET"
..$ url : chr "//www.washingtonpost.com/newssearch/"
..$ enctype: chr "form"
..$ fields :List of 1
.. ..$ query:List of 7
.. .. ..$ name : chr "query"
.. .. ..$ type : chr "text"
.. .. ..$ value : NULL
.. .. ..$ checked : NULL
.. .. ..$ disabled: NULL
.. .. ..$ readonly: NULL
.. .. ..$ required: logi FALSE
.. .. ..- attr(*, "class")= chr "input"
.. ..- attr(*, "class")= chr "fields"
..- attr(*, "class")= chr "form"
My particular case is to log in to this site, however the Washington Post's pop up log in seems similar enough that it would be the same procedure. How can I call these pop-up log ins?
*I am not too familiar with html, so if there are any better terms to use or ways to phrase it, feel free to correct me.