How about doing all the pre-bed "routines" IN her room. Only.
Not anywhere else.
Then, let her sleep, anywhere, but only if it is in her room.
(my daughter went through a phase where she'd sleep in her room, but wanted to sleep on the floor instead... atop all her blankets and stuffed animals). And we let her, We knew it was only a phase.
And, explain to her, that she is a big girl now... and can't fit on Mommy's lap etc. So... maybe get a nice comfy chair for her room where SHE can sit, while you read her a story or something. THEN, make the routine that she has to be in her bed or at least LYING down... while you keep her company in her room, sitting in the chair. Or, get her her own child sized rocking chair, where she can sit in and rock herself.
The thing is, she is used to the routine she has always been doing. So, now, it has to change... because her Mommy needs it. And yes, kids usually have a transition adjustment to make, with any "new" routine. So just keep trying... it will be repetitious, but that is the way they 'learn' a 'new' routine.
Try to do it, with NO "bribery." Otherwise, she will just get used to "having to have" a bribery, ANYTIME, you ask her to do something. Just use talking to her and logic, and communication, to 'teach' her. And then use repetition and consistency about it.
I know its not easy... but that is all she is used to now. So, she gets mad. That is the 3 year old mind.
Try to instill independence in her... have her walk to her room, for example, instead of being carried there or something. Have HER be a part of the routine... instead of an accessory. Have HER make a decision... or at least make it sound like it is her decision. Give her 2 choices: going in her room like a big girl and "helping" Mommy... or Mommy will leave. For example. And if she does not cooperate, then yes, LEAVE. Let her stew about it.. then go back and TALK about it. NOT "bribing" her about it. AND keep the lights turned OFF.
Try to make it like she is a PART of the "team".... call it "Team Sleep" or something. And have her have a role in it. Kids this age usually like to know they are "helping" Mommy.
For us, at bedtime, we do our routine: brush teeth, change into pajamas, my kids both walk to bed, we turn off the lights, and then we talk story and what not. But we keep EVERYTHING turned OFF and quiet. My son will sometimes get up and walk out of the room to "check things"... but that is "his" routine, we let him do it, and he DOES come back to the room and his bed in a few minutes. That is "his" thing. After he does that he is satisfied. Perhaps, let your daughter adopt a "routine" for herself... that is NOT being on your lap. She can tuck in her stuffed animals perhaps, instead. Just think of something. Something she does for herself... instead of to or on Mommy, for example.
I know, its not easy. But any change in routine for bed, will take time. Just keep to it, and be consistent.
Also try giving her a flashlight to keep in her bed. My daughter loved that, and still does.
All the best,
Susan