What was your daughter like at two and a half -- the age your son is now?
Was she as demanding as she is now, or was she mellower?
Just a thought: When your son is the age that your daughter is now, he may no longer be so mellow. So don't think of any of this, your daughter's behavior or your son's, as a fixed indicator of personality. That's an important starting point.
You also mention only briefly that you have a brand new baby (congrats!). Isn't it possible that her grumpiness with her brother is actually a reaction not to him as much as to the new baby? An infant that young is either constantly in someone's arms or asleep; she knows she can't get a rise out of a mere baby; but a toddler brother will react to her and she is longing for a reaction, so she may be taking out her jealousy of the baby on her toddler brother. In other words -- this may not be just about jealous of her brother but jealousy over the baby as well. She's got two more appealing little humans to share you with and she knows it well.
She is at an age where kids assert themselves as individuals. Add two younger siblings, one new, into the mix, and the assertion can take these kinds of negative turns. Are you familiar with the idea "negative attention"? Young kids do not really distinguish between positive attention (praise, etc.) and negative attention (being yelled at or disciplined). They often will act out just to get ANY attention and if it's negative that still fulfills some need for them. So: React less. Ignore more.
And be SURE you do things with her, all alone, and that your husband does too. You may be right that you are both focusing on your cuddly toddler and new baby much more than on her, especially when her behavior isn't nice. But that's when you have to push through the natural inclination to turn to the sweeter kid first -- you have to double down on more individual attention for her, the kid who's not sweet just now. Do things with her that are age-appropriate, things that "you can do because you're such a big girl." Get her out of the house and away from her siblings on a regular basis. Don't let her hear all the time, "We can't go there/do that/attend that because your brother has to nap at that time of day/the baby is too small to go" etc. I have seen so many families with two kids -- and especially families with three or more -- where the youngest child's schedule dominates everything for years and the oldest child always hears "we can't because the baby can't do that yet" -- please watch for that because it's more common than you realize.
Can you and your husband work out a schedule where one of you goes with her, just her, to a regular class like Music Together or Kindermusik or any class at a local rec center for kids her age? Can you get your husband to turn up to volunteer at or just attend an event at the preschool, especially unexpectedly during the week to surprise her? Find ways to give her extra attention and don't make that attention contingent on her "being good" or "being nice to your brother." She needs to know that she gets positive attention without strings at times, especially right now with an infant in the house, who gets attention 24-7 for doing nothing, in her eyes.
A reward chart? Maybe. But what will be the specific, concrete actions for which she gets rewards? A reward chart should be rewards for doing certain things, not rewards for NOT doing certain things. What discipline do you have in place for when she kicks or hits her brother? Is it swift, consistently the same every time, and does it remove something she really hates to lose? Are you constantly telling her "don't do x" and not telling her, "You did a good job on Y?" Are you distracting and redirecting immediately and firmly when she is on the brink of acting out -- and do you recognize when she's on that brink, or does behavior have to get to an actual grab or push before you realize it's happening?
Just some things to consider. She is in a tough place right now and it's not about permanent temperament, possibly, so much as a lot of jealousy and a feeling that she is not as big a deal to anyone as the baby and her cuddly brother. That's not an excuse for her -- she can't behave certain ways, period, jealousy or not --but it does explain things. Most of all - do not ever, ever let her hear you compare her to her brother. "He shared with you, he always shares" etc. will only make her worse, not better -- she will figure she needs to differentiate herself from him and if he shares, well, she won't be like him.....
Read some good parenting books that deal with siblings and sibling jealousies and the role of the oldest child. That may help a lot.
And you know that the water in the face act your husband did was "poor parenting" as you note, but does HE know that fully and will he commit to not doing that? It's not a huge leap from that to "You hit your brother so he gets to hit YOU so you know what it feels like!" and that sets a terrible precedent. I can see getting so frustrated in the moment I'd splash a kid like that too but I hope your husband fully gets why he can't do that again.