Tamim from Qatar was arrested in 2004 in London after he participated in a fight in a gay bar with his boyfriend, also Qatari. He was banned from going to the bar for 1 month. The news appeared in several major newspapers in London (if I'm not mistaken, it even appeared in DailyMail), but 1 month after the news went viral in London newspapers, all the newspapers that published the stories disappeared with the news. I think there's still a website that kept the news. Unofficial site of course LOL.
In 2019, a sexual connection between Abdullah Al-Athbah (the Emir's right-hand man) and Princess Gahliyah Al Thani (married) was leaked. In that call they had sex over the phone and even Gahliyah asked Abdullah if Sheikha Mozah (the Emir's mother) had already given up on him. Abdullah himself said, "Never. Never. Never." Then Gahliyah said, "Knowing her, she would do that. I know her very well. Shortly after, Abdullah says he's not Sheikha Mozah's type and Gahliyah ends by saying, "I know you're not her type, I know her type. her and I know who [he is].” Implying that Sheikha Mozah is cheating on the former Emir of Qatar, Sheikh Hamad. The leaked link is on YouTube.
I personally don't believe that Sheikha Mozah would betray Sheikh Hamad, not even for $1 billion.
There are also rumors that Mohammed and Khalifa are bisexual, though, no one can confirm. There are rumors that Mohammed dated Paris Hilton back in the day and that he preferred only white women and that he was bisexual. There are also rumors that Khalifa was bisexual and had a longtime girlfriend. No one can say either.