fhutts, I think we've crossed paths before on the various threads about 3 month ish old DCs struggling to sleep.
My DS is very similar - struggles to nap during the day, and isn't always easy to get to sleep at bedtime. He gets overtired really easily.
I agree with rubyslippers that overtiredness & overstimulation is probably the problem. We had to bin our bedtime routine as by the time we'd done a bath (or anything, in fact), DS was so tired that he would also flatly refuse to feed at bedtime.
What I've found is that he needs a nap just before bed, so that while he's tired enough to think it's nighttime, he has enough sleep in him not to be excessively overtired. So he will nap from any time between 8pm and 8.50pm, and then wake for his bedtime feed at about 9pm, even if he's only been asleep 10 mins. At that point, he will happily feed to sleep and get drowsy. If I try to do bedtime any sooner, or do anything other than nappy change / feed at bedtime, he works himself into a state instead of getting tired and drowsy.
Unfortunately his bedtime is reliant on him thinking it's nighttime, as the only way I can get him to sleep is to feed him to sleep, which he won't do if he thinks it's daytime (during the day he will only sleep in the sling - no good for getting him down in the cot, or allowing me to go to bed). And he doesn't think it was night time until 8pm - now 9pm as the clocks have changed.
My plan is to try to do a bath / bedtime routine, then get him to have that last nap, then wake him up and do a bedtime feed.
I know your DD struggles to nap, so trying to get her to sleep may be difficult for you, but it might be worth a try. DS is always harder to settle in the evenings (DH hates being on sling duty then!) but has improved in the last couple of weeks (he is nearly 13 weeks).
I'm also struggling to get DS into his cot without him waking & kicking up a fuss. I may try waiting for longer before I put him down, and then try to gradually put him down almost asleep rather than fully asleep.
And at least be cheered by the fact that your DD sleeps so well after bedtime - DS is up 3 times a night once he's finally down, and last night we were awake between 2.30 and 5.30am when he refused to go back into his cot (or to settle in bed with me)