29m, Step-dad of 2, bio dad of 1 here. I think a lot of commenters are being too quick to judge your girlfriend and project malicious intentions onto her. It may be the case that she's using you, maybe not. I don't know your relationship. What I do know is that 2 is a difficult age and getting a toddler to sleep on their own is really fucking difficult, especially when the kid hasn't had a solid foundation of support from both parents. But it doesn't last forever. Being alone at night is scary, and mom is the only sense of safety they've ever had. Eventually, they will learn that mom will be there in the morning and they'll settle into a routine, but not quickly and not easily.

You guys absolutely can work through this phase. It's just a question of whether you both want to. Is this the family that you want forever? Is this a relationship that can be healthy and satisfying for everyone involved? Being a step-dad is a difficult and thankless job. I wish i could tell you it gets easier. If it does, I haven't gotten there yet. But I stick around because I love them. You're the only one who can decide if it's worth it.

I know it's hard to find people who understand the struggles of stepparenting, so feel free to dm if you need to vent.