Corrine wasn't allowed children at all?

It's definitely a plot hole that should've been covered. Because of this, the grandmother hissing at Corrine at the Christmas party "Maybe some day you'll have a daughter of your own so that you can pass [the jewels] on to" doesn't make any sense. Corrine stating to the children "My father forgave me on one condition: that I didn't have any children with your father" is not enough. If that's so, she could've freed as soon as the grandfather died. So, her motivations are left unclear.

In the original film, it's more of a plot twist in which it's clearly spelled out that according to the grandfather's will, Corrine would be disinherited if it's ever discovered that she bore any children with her first husband. At that point the children realize that their mother never intended them to leave the attic.

Plus, in the novel, Corrine couldn't have any children from her second marriage either. So that was a double slap to Corrine from her father.

In "Petals" (the film) Corrine tells Bart at the Christmas party (in a great hurry) "You know my father, he was so hard on me. You wouldn't have accepted me. You would've put me out of his will". Still, it's more blink-and-miss.

That's a big foul in the new films. The codicil in the grandfather's will about Corrine being disinherited is vital in the book series and it's just merely (if at all) touched upon in the Lifetime films.

I think with her second husband she just couldnt get pregnant

as for her first marriage-he was her half brother. If she had children with him her father wasnt going to give her her trust fund and stuff because then she had kids made in sin/incset

hence locking them away

I'd thought Corrine kept her kids secret from Bart because it would've been an interesting surprise to suddenly explain four children from her previous marriage. (Children who'd until then been kept hidden in her mother's attic, for two years. )

Corrine began reminding me of Betty Draper from Mad Men, and not just because Kiernan Shipka's playing her daughter. 

Corrine's father, Malcolm, was a very cruel and controlling man. The codicil in his will stating she would lose everything if she ever had children, even in her second marriage, or if it was ever proven she had children in her first marriage, was his way of continuing to hold some degree of control over her life even from his grave.

BTW, he had a private investigator keep tabs on Corrine and Christopher without Olivia's knowledge. He knew they lived well beyond their means because Christopher could never deny Corrine anything, and he knew as a widow Corrine would lose everything. She had no skills, she couldn't even balance a checkbook, and she would have no choice but to come home to Foxworth Hall. He was also fully aware of the existence of their four children.

Malcolm knew Corrine was enough like himself to find a way to make those four children disappear permanently. He knew she would rather kill her children than walk away from the Foxworth fortune.