Death in the Family isn't a perfect story and even years later there's some confusion. One of the first arguments I heard from the DC comic fandom was if we actually got an answer to the question of who the real mother was.
The whole thing starts when Jason discovers his water damaged birth certificate and notices there's a "S" instead of a "C" at the start of his mother's name. He couldn't read the name due to the damage but it means Catherine Todd wasn't his birth mother but rather his stepmother. Jason was happy to discover he had a living parent and excited that there was a chance to meet her. Going through his dad's address book Jason found three names that start with a "S". Later on he admits to Batman he knows the chances are slim that any of them are his mom but he felt compelled to try.
It's a product of it's time as there are no DNA tests.
Sharmin Rosen, a Mossad agent is the first potential mom and Batman doesn't really get a definitive answer. Sure he asks her if she's ever been to Gotham city, which she denies, that however doesn't mean she wasn't the mom. Batman never says why he's asking her this question and if it's too personal she might not want to answer it. How did Willis even know her then? Never explained.
Somehow Willis apparently knew Lady Shiva too which again isn't explained. This has been debated by fans that think there's a potential for Jason and Cassandra to be siblings. The "proof" in the DITF story that Shiva isn't the mother has been retconned to make her Cassandra's mother. Batman asks Shiva if she ever had a baby which she gleeful lies about having several forcing Batman to give her truth serum. Under it she states she hasn't had any children. Much later on when Cassandra is looking for her own mother Batman mentions the encounter and the fact Cassandra and Jason are close in age.
I personally don't believe this sibling theory since I find it a real to strain to explain it in a logical way. Willis might have known her before she became Lady Shiva and was just Sandra Woosan/Wu-San. Jason and Cassandra are close in age as they were born the same year. (Cassandra in January and Jason in August. As I recently heard from another fan who noted which turned 18 first Cassandra is actually older.) The only way for them to be siblings through Shiva would be if they were twins. So assuming one of the birthdays is a lie that would mean Shiva would have to be with David Cain and Willis Todd around the same time. I don't buy for a moment that David would allow this during his "making a baby assassin" period or Shiva would intentionally screw up the deal.
Given what little we know about Willis I have trouble believing he could catch Shiva's eye enough that she'd risk everything for even a night of passion. And even IF that were the case why would David just reject another baby and decide to send the infant back to Willis? It makes no sense. I'd have an easier time believing Jason was the kid of Shiva's sister and she was dead before any of this.
Shelia Haywood was meant to be the mother but there really isn't a strong case for her in the story. The only reason we have to believe she is comes from Bruce thinking Jason has her eyes and her supporting the idea. She claimed she went to school after Jason was born and decided to leave Jason with his dad after Willis fell in love with Catherine. However Joker says she had to leave the USA after the death of a teen in an implied abortion Shelia helped out with. Was she lying to Jason? We never get a clear picture how much or how little she cares about him. Shelia was also embezzling money from the refugee camp she worked at and being blackmailed by Joker.
When Bruce enters her tent she knows who he is so it's not unreasonable for her to know of Jason and use that to try to weasel money out of Bruce. What many think is the most damning evidence of her not being the mom (besides her using him to get in Joker's good graces) is her dying words being that Jason must have really loved his mother. This lead some fans into thinking Sheila was admitting she wasn't the mom. While others think she might have been admitting that Catherine was his true mother for caring for him and Jason was simply projecting that love for her onto Shelia. I tend to agree with the latter but I would be fine if Sheila wasn't the mother either.
In current canon the suggestions of Willis being a player are confirmed. Catherine was the mom in New 52 although how that works with the DITF story is sketchy. There have also been titles that suggest old canon rather than the Catherine angle like Damian saying Jason's mother betrayed him where she seemed more innocent in Jason and Joker's accounts. Jason also told Isabel that an innocent woman never died on his watch which sounds like the mom in question did sell him out.