In the US system the Courts are independent. Politicians can't formally influence a judge. Politicians are supposed to shut up and let justice take its course. They have no legal power in the court case.
However politicians have a platform from which to criticise a court's decision. The can speak to the media, they can hold public meetings. And because of their public role, they are more likely to be listened to than a random person.
In theory the Judge should not be influenced by this (and judges are trained and are proud that they aren't easily swayed by anything but the law). Judges are supposed to follow the law, and not public opinion. In practice, judges are human.
In the USA, for a federal judge who has been failing in their duty to reach a fair decision, Congress does have the power of impeachment. This is rarely used and not simply because one set of politicians disagrees with a judge. It can be used when a judge has, for example, been corrupt. Congress can impeach, and if the judge is convicted in a Senate trial, they are removed from office. Impeachment and conviction is made intentionally hard. A simple majority can't convict on impeachment charges. The impeachment process is not intended to be abused to remove judges who are lawful and dutiful, even if that duty brings them into conflict with one group of politicians. So far, the impeachment process for judges hasn't been abused in this way.
This impeachment power is irrelevant to the Rittenhouse case, as the court is a state court, not a Federal Court. However Wisconsin law has procedures to remove a judge who fails to serve justice.