My 4-year-old daughter got in trouble for biting today at school. She's been struggling behaviorally in school for a while now. I'm not sure if it's appropriate to take toys and TV from her and if so how long? I'm just sort of at my wits' end in general and I'm worried I may be punishing her the wrong way making things harder.
At four, there's not a lot of point in "later" punishments. Your child isn't thinking about long term consequences; she is acting in the moment, primarily.
Issues like biting need to be handled in two parts. One, they need to be handled in situ when they occur. That's going to be up to the daycare/school, of course, and you might want to talk to them about how they handle it at the time. In particular, you can talk about how you and they can handle biting situations identically (when it occurs at home or out with you).
Also, though, make sure that the daycare/school is doing the right thing when it happens; removing her from the situation, getting her to a calmer place, rather than attacking her mentally (or physically, god forbid) and making the situation worse. She's biting because she's stressed and frustrated; they should be taking steps to reduce the stress in the situation, not increase it.
Two, you need to work with her to give her tools to handle being frustrated. That is something many children struggle to deal with; often the options are lash out or bottle it up inside, and neither of those are good (and I'd say bottling up is probably worse, at that age). Talk with her, at a relatively mature level, about how she can handle being frustrated. Role play with her. Show her in your behavior how to handle being frustrated, and point out to her both when you do so effectively and when you fail (afterwards, of course).
The key here is to treat this as something she needs to learn, not something she needs to be punished for. She is four years old, and having problems with something that many adults still have problems with (if not the precise same response, very similar). Give her the tools to handle frustration now, and she'll be a much better person for it - and hopefully lessen, or stop, the biting incidents.
I think you are making a mistake by focusing on punishment. Your goal is a better response to frustration. Punishment might be a part of your plan, but then again, it might not.
You need as much information as you can get about what led up to the problem an how the school handled it. Then you need to work with your daughter to react in an appropriate way. Repeated role-play with her, going through the situations so she can practice how to deal with her frustrations.
Kids this age act irrationally. They're uncivilized and it's your job to teach her how to be a decent human being. Rough-housing at home is a great way for kids to learn rules about physical interactions so they can be properly socialized. Most kids are starved for this kind of play and it's absolutely crucial to their development. When kids start hitting or biting during rough play, the play stops abruptly. This teaches your child that if they want to have fun, they have to play by the rules.
Rough play should come naturally to you as a parent, but if you are worried about the risks or the rules there is plenty of material online to point you in the right direction. Here's an article from a quick google search: https://raisingchildren.net.au/preschoolers/play-learning/active-play/rough-play-guide
With my kids it usually involves lots of wrestling, tossing the kids onto the couch, and lots of tickling. Dads are good for this sort of play because they're usually good at letting the kids take some risks that mom might not be okay with :-).