The average age for a girl to be potty trained is 35 months. Which means half of girls aren't trained until after that. So she's not really that far behind. (And many kids show a passing interest in the potty long before they're ready to go, so baby may have very little to do with it).
You don't want her controlling you. Take away the control issue. No more talk about the potty. Just drop the issue entirely. She may decide, once it's no longer an issue, to go potty. Or she may not.
I went through this same thing with my son. He showed interest in the potty, and a baby was on the way, so I was excited to get him out of diapers. But it was just that passing curiosity. I pushed him to go, tried all the same things, rewards, threats, etc, and was very frustrated. Did this for about a year and a half. I finally had enough, put him back in real diapers (not pullups) and stopped asking him if he needed to go, telling him to go, commenting about going potty when he needed a change, etc. I did decide that playing the Nintendo was a big-kid thing, and big kids wore underpants and went potty. The only time I ever mentioned it was when he asked to play, then I just said, "oh, I'm sorry, that's a big-kid thing, and big kids wear underpants and go potty." After a few months he decided to go potty, and he was 100% trained within a week! (And I did very little in the process.)
As far as preschool, many good programs understand that not all 3-year-olds are ready to go potty. The don't expect to change her, but if you let them know, they may be willing to work with it. (And many 3-year-olds, and even older, have accidents at school anyway, so they should be kind of used to it anyway). Plus, hopefully it's only a 3-4 hour a day program, and she may not need a change at all. For some kids, being in the environment where other kids their age go potty can be a big incentive for them to start doing it too.
Hang in there! This will pass before you know it!