Before we deal with the training pants question, here's link to one of the best articles on assessing a child's readiness for toilet learning.
I wish I'd read this long ago; it would have saved myself and some sweet little kids a lot of heartache and frustration.
Kids have lots of their own reasons not to use the toilet. One very real thing I'm also going to mention is what I've witnessed myself, lots of times: a family, expecting a second child, decides to toilet train the first. While there's one child in the picture, things go swimmingly. When baby #2 comes along, however, the oldest often regresses. This will usually happen if: 1. the child wasn't necessarily ready on their own to use the toilet or 2. The child has decided to regress (become more babylike) and not use the toilet (because the new baby doesn't use the toilet), thus messing their pants.
If it were me, I'd do an assessment and also try to create an open-ended dialogue about what it is that your daughter might be disliking. Some children are resistant because it pulls them away from what they want to be doing, namely, playing. Some children really don't like to sit on the toilet, and the questions about "Do you need to go potty?" trigger an emotional response. For both the parent and child, the feelings can be deep, as evidenced by your response.
When you feel she's ready,put her in clothes/diapers she can feel wet in. I'd shun the pull-ups, unless you are traveling: they don't let children feel themselves getting wet in real time. If you have cloth diapers, those are great for teaching kids what wet feels like. If none of these options work for you, then yes, maybe it is time to offer training pants OR diapers. (Pull-Ups often confuse kids because they look like underwear and feel like a diaper.) Get the superthick ones...you can double them up, or put a plastic diaper cover over them to contain leaks.
I also want to say that I've know several kids who began mastering the toilet as 3 and 4 year olds. It was when they began seeing other kids using the toilet that they decided they were ready to try and follow the pack. Their parents relaxed approach to this really helped, and contrary to popular opinion, there are some great preschools out there (mine included) that are perfectly happy to have toilet-learning 3 year olds start with them.
I hope some of this helps. It's a hard place to be in, to have to decide when to encourage/nudge our kids and when to hang back a bit. My best to you... oh, and one more thing--keep a basket of books or toys handy by the potty. Lots of adults like to read on the toilet, so do kids!