I have a 2.5 year old and she definitely still needs her nap, although she doesn't always agree : ) . You didn't describe your usual routine or what time she naps or sleeps at night so it's a little hard to compare our situations, but here's our deal. Over the last bunch of months my little one needs to take her nap EARLIER. Yes, earlier, completely the opposite of what everyone will tell you and what everyone else's kids do. If I don' t get her in sometime between 11:15 and 11:30 she is a disaster and resists naps because she is overtired. We call it her "sleep window" and it's quite narrow and shifts often. She used to nap closer to noon like everyone else but it just got to be earlier and earlier. For us, good sleep begets good sleep and her naps and nighttime sleep BOTH have to be good or we are in trouble. I agree a routine is helpful - we don't really have a big one but I do start telling her when it's getting close to nap. In fact, she's in there right now and I think I missed her sleep window as she's still talking away. I am lucky she's still in the crib so she's stuck in there whether she sleeps or not.
My last resort is a walk in the stroller. If she hasn't settled down to nap by about 1:30 or 2 on those disaster days I put her in the stroller, recline it all the way and take her walking for about an hr and a half and she'll (usually but not always) sleep then. looks like I might have to do that today.
Oh and BTW, my nanny, MIL and my mom have a MUCH easier time getting her to nap. It's when Mommy's around that she's more resistant. I do work full time away from home so weekends are when I get to deal with it!
Anyway, good luck to you, I agree you should do your best to not scream back but I know how frustrating things can get. Nobody's perfect.