It is common for children to stop napping at around 3-4 years old. My 3.5 year old is almost like yours: doesn't nap for us most days, naps for daycare. He also sleeps pretty late - 10pm is common - and wakes up by 7am (we wake him up). He just doesn't sleep all that much. Is that okay? Sure. Is it optimal? Nope... but such is life.
What we have had success with nighttime is a few things.
First off, she is old enough to likely be better off not cosleeping (unless your space requires it). Sleeping with someone else in the bed is hard; it requires dealing with that person moving about, kicking, who knows what; even a calm sleeper still breathes. If you can, I would consider seeing if sleeping in another room would help - it definitely helps my children, when we have to share a hotel room vs. have a suite there's a big difference. Children don't need much - a sleeping bag on the floor would be a lot of fun likely as a trial. Hard surface isn't at all a problem in most cases! You can still lay next to her to help her go to sleep.
Second, make sure you have a very strict routine. Bath if you have one, toothbrush, potty, books, bed - do it all in the same order every day, and have rules for how each one is done. Routine is very calming for children.
Third, develop strategies for dealing with the frustration that avoid you getting to the boiling/yelling point. I have a 3.5 and a 21 month old. I know how easy it is to get frustrated, trust me. Sometimes I get to the point that I have to swap with my wife; that is a very effective strategy, because she's calm entering the situation and the change often calms the children. A frustrated parent is an ineffective parent.
Otherwise, I have boundaries and I try to allow the children to do some things within those boundaries. If they need to run around a little, I tolerate that - as long as they understand the rules (has to be at least sort of calm running, if one is in bed no bothering that one, etc.). All of the lights are off - no nightlights if they're active. Nightlights only come on when they're settled. (And by all, I mean all - no light in the house, all curtains drawn).
Fourth, see what you can do about various near-bedtime activities. No screen time within half an hour of bed - most screens have a lot bluer spectrum that keeps people more awake. Dessert is good as long as it's not chocolate heavy - sugar makes most people sleepy. Full tummy is also good - cheese stick, carrots, that sort of thing.
Finally, sometimes I find music helpful; either played from a speaker of some sort (phone, radio, whatever) or sung with the child (you'd think that would make it worse, but it seems to calm them).
