Joan said she felt “knocked down” by the news the singer had been rushed to hospital on Tuesday, after she was found unconscious at her Hollywood home.
She also revealed Demi had helped her son Frankie with his sobriety, having previously overcome drink and drugs addiction herself.
In an extended Twitter post that has since gone viral, Joan wrote: “I am knocked down over Demi, I hope and pray that she recovers quickly and finds sobriety again.
“It is work, hard work, but with support and love, she will succeed! I know it, we are there for her in any way.
“She is a sweet, kind person who have, in my personal experience, always shown love to everyone in my world. She was there for Frankie during his work with sobriety and as we know, he just celebrated his ONE year.
“She has always been so supportive of Ariana as well, sharing her experiences with the fame and celebrity and notoriety of growing up in a very public space…women supporting women, what a fabulous idea! Yes, it can happen and does!”
Joan then appealed for people to be more positive and kind to one another.
She continued: “SOOO, in light of my introspection today, I will be yet another voice on social media imparting an idea I came up with … let’s ALL make a deal today … let’s try to be nice to everyone, let’s try to remember that we are ALL human and no one is better than the other, let’s try to share love and light, let’s not pass judgement. Let’s not amplify negativity by repeating it.
“Remember, if you have nothing good to say, why say it?? Don’t say it! You never know how much you are hurting someone. Try not to find your own self-worth by knocking down others. You never know, if you share love and light, that just may give you the self-worth you are desperately looking for.
“No one person knows what another person is going through, so why not support instead of tear them apart? Remember, not one fan base is better than the other, love and support who you love, but not by knocking the others. What is the point? Do not pit one person’s achievements against another. Why not just celebrate the achievement?
“It’s a lot, I know, but just try it today!! Maybe you will feel so good by the time you go to sleep tonight, that you may want to do it again tomorrow. It’s work, but honestly, what is worth having that you didn’t work for? Let me know how you do. Sending love.”
Both of her children then shared the post on their own Twitter accounts, with Ariana writing: “Mom wrote something beautiful. check it out. much love.”
After retweeting the message, Frankie added: “Still in shock about Demi. She is a dear friend & a huge part of my sobriety. She was there for me in the beginning & her strength gave me strength. Now i will stay strong for her in this difficult time.
“I love you Demi. I’m here for u & anyone else struggling with this disease.”
Demi is said to be awake and with family at the Cedars-Sinai Medical Center in Los Angeles.
Her spokesperson told the BBC: “Demi is awake and with her family who want to express thanks to everyone for the love, prayers and support.”
They added: “Some of the information being reported is incorrect and they respectfully ask for privacy.”