I also have a 3-year-old daughter with sleep issues. I asked my pediatrician about it and he said that as long as they are getting 10 hours of sleep a day (including naps if they will take them, then that's all they need). Now this is a tall order in my house. My daughter resists naps too on the days when she's home and I am told she doesn't often nap at preschool, which makes for a GRUMPY girl when I get her home at night.
What helps us is to start her evening ritual earlier, but keep her up later and keep it VERY structured and VERY consistent every single day, even when we are out of town. For instance, Give her dinner between 5:30 and 6, let her play for an hour, then bathtime no later than 7 for half an hour. I use a kitchen timer that beeps to let her know when it's time to move from one activity to the next. That has REALLY helped! I also do not allow ANY TV or computer after 7, so we can spend the next couple of hours winding down. That means no TV for us either, which ultimately forces us to spend some quality time together without distractions. You know she's tired, so the trick is just keeping her busy, but keeping it predictable too so she has no chance to manipulate the situation when bedtime comes.
After my daughter's bath I do an activity with her that is just for her (I have a 4-month-old daughter as well), like painting her toes or braiding her hair or something she really likes to do that is special. Then at 7:30 we have a little snack like milk & animal crackers, brush teeth and get in the bed at 8 for story time and lullabies, which lasts around an hour. We read 5 stories, and she knows she only gets 5. Then we turn the lights out and we have 3 lullabies, and she knows after 3 she goes to sleep. She also knows we do not get out of the bed once the lullabies are over, so I have to make sure she goes to the bathroom and has her water by her bed BEFORE we get in it.
The key is the wind down time. Make sure she understands that this is quiet time for everyone, not just for her. This might be hard because you have older kids too, but in order to get it to work, EVERYONE has to participate. She wants to be part of the party and won't settle down as long as she knows there's activity going on. Mine often makes excuses (we've heard them all) as to why she can't sleep (has to use the bathroom, needs water, has a tummy ache, is hungry). Of course you know she's just trying to stay up, but don't let it get to you and really try your best to ignore it. If she screams and cries (like mine often does), just do your best to ignore it (my pediatrician even told me that!). If she gets out of the bed and plays, make sure the room is completely dark so she can't see and put her back in the bed. Just keep putting her back in the bed! Mine likes to talk to her 'buddies' often until after 10pm. Finally, I started going in her room and telling her 'buddies' to settle down and be quiet so Sofia can get some sleep. I can't believe it, but it works!
I realize I can't force her to go to sleep, but I can do everything I can to make her evening and bedtime ritual as relaxed and structured as possible. I don't give her too much freedom because as you know, a three-year-old will use that against you. It stinks to have to micromanage them, especially because it means you have to give up some of your freedom at night, which I know is precious, precious time, but I have found that 5 out of 7 nights a week, the structure works and she sometimes even sleeps in until 7 am! (woo hoo!)
Good luck!