One of the biggest themes of the Gilmore Girls revival has been the death of Richard, played by the late great Edward Herrmann, who died of brain cancer in 2014. This death was obviously huge in the lives of Emily, Lorelai, and Rory, but particularly for Emily, given the fact that he was her husband for the majority of her life. But Emily is dating again on the Gilmore Girls revival, and that's actually really good for her, even if it totally freaked out Lorelai.
As Emily reminded her daughter and granddaughter several times throughout the four episodes, she was married for 50 years. Richard was half of her, and she doesn't quite know what to do now, or what to do with her life. She started first with The Life Changing Magic of Tidying Up, which didn't work out very well for her. And then she tried therapy with Lorelai, which didn't work out very well for her either. Finally, on the unveiling of the fifth try to get Richard's headstone correct, it looked like she'd gotten started trying to move on with her life. She started dating Jack Smith, a man who she said she'd been friends with for over 30 years, and who was at Richard's funeral.
Lorelai, of course, did not react to this very well, and was understandably very wigged out by the whole idea of her mother dating another man, especially so soon after they had buried her father. Then again, look at where Emily was just a few scenes ago. She wasn't getting out of bed until noon. She was eating in front of the TV in her living room. None of these things are necessarily bad in and of themselves, but they are certainly not Emily Gilmore. The woman we've come to know has a heavily regulated routine to her life, and it does not normally involve falling apart and sleeping until noon. Emily Gilmore eats in the dining room.
The fact of the matter is that no one, not even Lorelai, gets to say when Emily is ready to date again, or to say who is or is not a "gold digger." (Yes, that was a Kanye West reference.) If this is what Emily needs to get a grip on her life, then I say good for her.