hi!
this may not be what you want to hear, but maybe you'd have a lot less stress if you dropped her nap alltogther?!!
My DD1 is 3years 2 months and she hasn't napped since 2.5 years old. She is on the lower end of sleep needs and by 2.5years so was definitely ready to be not napping. The signs that it was time to drop it were that she wouldn't settle at bedtime (like you're describing), was waking early in the morning (as early as 5am some days adn couldn't get back to sleep) and even some NWs which were totally out of character for her. I found that because she was going to bed so late, she was getting less sleep overnight, so was tired the next day...tired enough to have a nice long nap...that would then mean bedtime issues and late night again etc etc. I actually found she was MORE well rested without a nap because then her night time sleep remained in tact and she was refreshed after a really long night sleep.
however before you freak out and stop reading my post because the idea of losing the nap is too hideous
there can be some really good advantages to having them not nap.
1/ my DD (who remember is lower in sleep needs) did a 13 hour night for quite a while when she first dropped her nap...so she was asleep by 6:30pm and didn't hear a peep till 7:30am
2/ she was asleep in about 2 minutes at bedtime so it made the double settle (my DD2 was about 6 months at the time) much much easier...i only needed to lie DD1 in bed, give her a kiss and she was virtually asleep
3/ i had a lovely LONG evening to myself which i think was actually better than having a break in the middle of the day with her nap, but then having her up half the evening and going to bed frustrated after only a short amount of time to myself
4/ i no longer have to work around her nap anymore, so its just DD2s routine that i need to consider
5/ no more stress trying to line both of their naps up and frustration when it didn't happen
Since she has stopped napping i have introduced a 'rest time' where i give her a cup of warm milk and a little snack (it was a pretty tempting one at the begining to really encourage the rest time), i put a timer on in her room (hot pink egg timer) for about an hour (it was shorter at first), put a story CD in her music player (playschool stories, in the night garden, bananas in pajamas etc) and get her a few nice toys and activities set up on the floor etc and then i tell her she doesn't have to sleep, but she does need to stay in her room and play quietly. she does REALLY well with this. She loves her milk drink and really looks forward to her rest time now. She gets to come out and watch one TV show (usually Hi-5) episode after her timer goes off. So i get about 1.5 hours without kids every day. The good thing is that its super easy to match this 'rest time' with DD2s nap in the middle of the day. I usually get DD1s rest time snacks and toys ready first, put her in her room with the timer on, then go put DD2 to bed and i have a nice long block of time to do what i want. Admittedly its not the same as when you KNOW they are both sleeping and nobody is going to bother you...! and she does come out of her room at times but i just say that if she's having trouble having a nice rest time then it must be because she's tired and i'm happy to come and put her to bed if she would rather that (she wouldn't...so she goes back to play). But overall it is way less stressful and she is out like a light at bedtime and i know i have my evening to myself.
When i was at your stage and DD1 had first dropped her nap, i would put DD1 to bed first and then put the baby to bed, because i knew i wouldn't hear another peep out of her she went to bed so well without a nap. Then it didn't matter how long it took DD2 to go to sleep, or if she protested or cried or whatever when i did shh/pat etc because i knew DD1 was totally out to it.
anyway, sorry for my ramblings...just seems like you might be coming to the end of the nap and it may not be as bad as it first seems (it is an adjustment though). Is your DD usually on the higher or lower end of sleep needs?
you might be seeing OT behaviour and that might be making you think she still needs the nap, but you may find she is much more well rested without the nap and will be less OT when you drop it (although no doubt the last hour or two of the day will be a bit crazy/emotional when you first drop the nap...but i found after a month or so she was fine right through to bedtime).
good luck, hope you work out a way to make things work for you
Jessie