This is all stuff you need to talk about with her parents, not us. Have you sat down with them and told them exactly what you say here? You say you've talked to her mom -- but was it a quick chat at pickup or dropoff, or a phone conversation? You and she need a long sit-down without any kids around so you both will not be distracted.
A few things to think about:
This change seems very sudden. That's not good and usually means the child has had some sudden change in his or her life. What's going on? Problems between mom and dad? New job for a parent, so she's angry at less time with that parent? New sibling or a sibling who has issues and therefore gets lots of attention for acting out (so sister is acting out too)? Could the girl be ill? Or starting to show reactions to allergies? Has her diet changed? (Some food dyes can actually make young children behave differently, so if she began eating foods that she had not had previously and they had dyes -- especially certain red or yellow dyes-- that actually could be part of the behavior change.)
Are there changes at the day care you run? I'm assuming you do run one since you refer to "my other children" here and it seems you're watching other folks' kids. Have new kids come in over these past few weeks, so she is trying to get more attention? Has the food changed, or is the whole routine being shifted around because of the holidays? Examine everything both at home and at day care. Kids can be very sensitive to things that adults brush off as no big deal. As for her adoring your daughter, I bet your teen is never the one to discipline her, so the girl sees your teen as an angel. Kids tend to take those of us who must say "No" for granted and adore those who are mostly just fun with them.
Yes, as you note, this also could be a change to her body's nap schedule that is making her over-tired and very fussy. Around two to three years old, MANY kids give up their daytime nap and go to no naps at all, even if their bodies really could use the rest. Does she actually nap at naptime or does she fuss and thrash around? Do you give her quiet activities to do if she won't sleep so she's not frustrated by feeling she's "forced" to nap when she can't? Or does she fight sleep and then just collapse into sleep?
Talk to the parents -- has her nighttime sleep changed? Is she sleeping less, going to bed later because something's diffferent at home, getting up earlier on her own? That needs to be accounted for somehow in her napping, or lack of it.
Find one consistent discipline. As another person who posted noted, you are trying lots of different things and she needs to know what's coming. If it's time out, can you really enforce it well if you are watching other kids, or is it too easy for her to slip out of her time out spot?
Do the parents see the same violent thrashing and hitting and kicking at home? That is the biggest red flag. Does she show remorse afterward? Does she get upset if she is told that "It hurts Billy when you kick him" because she understands what it means to feel hurt? If she is showing some empathy, and most kids this age can do that, that's a good sign, but if she is raging without any empathy afterward, she might benefit from some evaluation. But the anger is so sudden that I really wonder if there are changes that you aren't aware of at home, or changes at the day care that seem normal to you but aren't to her (especially the introduction of any new kids).
It is very typical for kids of three to start being more defiant, saying no a lot, not caring what their adult caregiver says, etc. This is the child developing a sense of self and asserting that. But the sudden addition of tantrums so violent you have to hold her is worrying. You and the mom need to work on it and talk daily -- are you reporting to her each day since this change?
Ultimately if the girl continues to kick, hit and spit, you may have to remove her from your day care because other parents are going to be upset and remove THEIR kids if they come home with bruises or say that the girl spit on them repeatedly. Let's hope that does not happen. It sounds like she is somehow very stressed all of a sudden. But you need much more work together with the parents to find out why, and more consistent discipline. And finally -- be certain you are never giving her "negative attention." If she gets more of your attention when she is behaving this way, she will learn that behaving this way gets your attention, so ensure that you remove your attention as much as possible.
