As for Peach's parents:
King Toadstool appeared most often in the comic books, looking like this:
He looks somewhat Toad-like, though it was shown on at least a couple of occasions that his mushroom cap was a hat (and sometimes a cake). He was also seen in a coloring book, looking similar, though a bit more human:
A totally human (after re-evolution) depiction of the Mushroom King was seen in the movie (though in the movie, he was the father of Daisy, not Peach):
Of course, he spent most of the movie as the fungus covering the kingdom after being de-evolved by Koopa. Interestingly, in the novelization, the Mushroom King was called "King Bowser."
Side note: Peach and Daisy are cousins, confirmed in Prima's guide for Mario Kart Wii, which matters because Nintendo Power stopped making guides and Prima is now Nintendo's official guide-maker.
Nintendo's Mario Sunshine website said that Toadsworth is Peach's father. In Mario Superstar Baseball, Lakitu says to Peach, of Toadsworth, "Your grandpa?! Oh, pardon me! Venerable Toadsworth!" Draw from that what you may. Factor in the appearance of Peach's grandmother in SMRPG:
Also, here's some interesting SMB-era artwork that may or may not be somewhat official, depicting the King, possibly the Queen, and Peach with a mushroom cap:
By Baby Bowser do you mean Bowser Jr., the Koopa Kids from some Mario Parties, or the baby version of Bowser seen in Yoshi's Story, Yoshi's Island DS, and Partners in Time?
For Bowser himself, his mother was seen briefly on the Super Show, as seen below:
Bowser's father was mentioned in passing in the comics twice, and was apparently at least presumed to be alive at the time, as Bowser said he hoped to see him on TV on
Kingdom's Most Wanted. He once told his son that "there's no problem too big to run away from." So yeah, Bowser probably has some issues. Common fanon is that Bowser's father's name is Morton, explaining why one of Bowser's children is Morton Jr.
Note that the Psychopath thought of the Magikoopa you fight as a boss in SMRPG (who is probably Kamek) is "That's... my child?" (presumably referring to Bowser) As seen in Yoshi's Island, Kamek seems to be something of a father figure to Bowser, though this is probably in the absence of his biological father.
Also note that, according to
Ignorance is Bliss, Bowser has a younger sister who reads a lot.
As for Bowser Jr. and the Koopalings, I have my own theories (which are also connected to my theories on the Koopa Kids from the Mario Parties), but there's very little to go on in the way of official sources. Nintendo Power UK was the first to posit the existence of "Clawdia Koopa" as the Koopalings' mother, and the movie gives us Lena as Bowser's wife/concubine/whatever, and the only other source is the ending of Sunshine, where Bowser tells Bowser Jr. that Peach is not his mother.
