No, at least in the Mario franchise, Peach has never had any children with Bowser. She is well-versed in the Super Mario franchise.
Bowser is also not related to Princess Daisy from the Mario Kart series. They are both characters created by Nintendo and used in their games.
Bowser Jr.'s mother is Princess Peach. Junior is informed by his father that Peach is his mother, but she is abducted by "bad" Mario during Super Mario Sunshine, according to the Super Mario wiki. This leaves Bowser as Junior's sole parent and he becomes very protective of her.
Bowser Sr. died when Bowser Jr was just a baby. He is now buried in the family graveyard on the top of Mount Crumpit.
Here is where things get a little confusing. According to some sources, including two official video games, Bowser Jr survived his father's death at the end of Super Mario Sunshine. However, other sources claim that he was killed off-screen by his father. The truth will probably never be known for sure, but for the purpose of this article I will assume that Bowser Jr survived his father's death.
Now that Bowser Jr is grown up, he has become the new king of the Koopas. King Koopa is currently serving as an advisor to Bowser Jr. They are both seen smiling in one scene from Paper Mario: Color Splash. This suggests that they have reconciled their differences at least temporarily.
In Mario + Rabbids Kingdom Battle, after defeating King Boo, it is revealed that he is actually Bowser's dad.
Bowser Jr.'s mother's identity is brought into doubt as early as his appearance in Super Mario Sunshine. During the story's events, Bowser Jr. informs his kid that Peach is not his mother, which Jr. then tries to prove by saying that she is after he defeats her in a battle. However, this claim is later revealed to be a ruse when Peach returns to the game just before she was supposed to die. Now that Peach is safe and sound, Jr. has no choice but to admit defeat and thank her for saving his life.
However, this does not mean that Bowser Jr.'s mother is none of your business. It's possible that we will never know who Bowser Jr.'s mother is because there are several characters in the series who have assumed different roles over time. For example, Waluigi is used by Bowser Jr. while he is still controlled by him and then given to Princess Peach after he is defeated. As you can see, this means that Waluigi has been at least two people during his lifetime: one who is controlled by Bowser Jr. and another who is controlled by Princess Peach.
Now, it is possible that Waluigi's true owner is neither Jr. nor Peach but someone else entirely.
Peach was adamantly opposed to marrying Bowser. The entire time, she is depicted resisting. As a result, the games are presented through Mario's delusory perspective. Peach and Bowser are in a serious relationship, and Mario is always attempting to split them up. Depending on the game, they're sort of dating. They just never officially married.
Bowser was once again inspired by Princess Daisy to try and win Peach's heart. He decided to do this by making an attractive package and sending it to her house. When she opened it, she found a flower necklace inside with a note saying "Will you be my wife?". At first, she was pleased but soon realized that he was trying to steal her crown. She didn't want to marry him so she sent him back the ring. Later on, when he brought up the subject again, she told him she had changed her mind about getting married. In some cases, she even tells him she has fallen in love with someone else (usually Luigi). He then tries to force himself on her but she gets away from him every time.
In some cases, she does agree to marry him. This usually occurs when there is no other option available so she can stay out of trouble. For example, in Super Mario Bros. 3, she is held captive by King Koopa and needs to be rescued by Mario before she will marry him.