The Boxcar Children/WMG

Boxcar Children: The Xerox Generation
Henry James Alden of the original Boxcar Children series becomes the grandfather of the four children in the newer books - who happen to, incidentally enough, have the same names and similar personalities to that of him and his siblings.

Henry is hallucinating the whole thing
I admit to not having read these books in a long time, but as a child, I noticed several inconsistencies in Benny's age, but none in the others. He gets older and younger sporadically, while his siblings age normally.

After the deaths of their parents, they were sent to an abusive orphanage. Benny was killed, either accidentally or intentionally. Henry convinced the girls to escape, but unfortunately, Violet got sick and died. (In the first book, she was taken to Dr. Moore and recovered, I'll explain why he wasn't there later.) Jessie gave up on their escape and returned to the orphanage, eventually becoming adopted by The Woman Who Owns Watch.

Grieving, Henry turned to drugs. He created a hallucination-refuge for himself in which all of his siblings survived. In reality, he is taken to an insane asylum, where Dr. Moore is his psychiatrist. Because Benny died first, and Henry doesn't remember things too clearly these days, he has the most inconsistencies. Henry also creates a life for all of them: rather than taking his sister, The Woman gave him a dog. (Jessie is Watch's closest companion.) Dr. Moore, his psychiatrist, took pity on them and gave Henry a job and later saved Violet. They had a grandfather who took them in. (It's possible that Grandfather existed early in Henry's life, but died when Henry was young. Either way, he was not there to take them in when their parents died.)

This also explains the inconsistencies in the characters "created" by Henry without a template from his own life such a Soo Lee (whose age changes similarly to Benny's) and Joe and Alice, who can't seem to decide if they're the aunt and uncle or cousins. They may have been based off of people Henry knew in the asylum, but he can't figure out how to incorporate into his delusions. Aunt Jane's sudden personality shift marks Henry's improvement. He was eventually released, but kept the innocent fantasies, which explains why they suddenly changed what time period they were set in. He's now wandering around modern times, adding what he sees to his fantasy world.
 * That was pretty much the most awesome four paragraphs I have read in my entire lifetime.

The kids killed their parents
They're dismissed as dead pretty quickly. There is never any explanation. Or maybe Violet did it and is not as innocent as she seems, and the others covered her either in fear or for the hell of it.

The kids are all Time Lords
Their TARDIS, of course, is the Boxcar. Watch is their companion.