Politically wounded by the rejection last month of her nominee for chief judge of the state Court of Appeals, Gov. Hochul has to remain strong in her dealings with the Legislature on the budget. Especially vital is her support for amending some of the criminal justice laws to better protect the people and giving more children the chance at a good education by raising the cap on charter schools.

There are strong vested interests opposed to both measures, and in negotiations with the governor, they may have the mastery. But Hochul insists she’s no pushover.

“It’s a rough and tumble job for a woman, but I got steel running in my veins,” she said in her inaugural address. Now she has to prove it. And if it takes digging in her heels and going over the April 1 budget deadline, so be it.

Issue No. 1 is crime. Oh, it’s not so bad, some say; it’s nothing like it was in the early 1990s. That’s true; it’s not — yet. But the rate at which crime is increasing is worse than it’s been in decades. Those who were around in the high-crime era see where things are going, and those who weren’t can easily believe they’re worse than they’ve ever been.

Some of the lawlessness has no easy solution. The state legalized marijuana without seriously restricting its sale, so we’ve been inundated with hundreds of illegal pot shops. Given their inventory and their reliance on cash transactions, they’re a magnet for robberies. Last Saturday a 20-year-old employee of a smoke shop in Richmond Hill was shot dead in one. He should have lived another six decades or so, but nope. Some unknown amoral person, armed with an all-too-common firearm, made sure he wouldn’t. And the state didn’t do all it could proactively to prevent it.

What in particular could it do? Give prosecutors the resources they need to take more cases to trial rather than offer weak plea bargains. Also let judges consider how dangerous someone is when setting bail — the way it’s done in all 49 other states and the federal system. That’s something Hochul wants. The leaders of the state Legislature, who apparently don’t mind rising crime, stand in the way.

The other thing many in Albany don’t seem to mind is the deterioration of our education system. School spending explodes — New York’s is the highest in the nation among municipalities of any size — yet too little of the money gets to the classroom. Instead it goes to the administrators and consultants; it’s amazing how many of each there are today. And then we graduate kids who can barely read.

What’s the best answer we’ve come up with so far in the public school system? Charters. Charter school kids, on the whole, wildly outperform those in regular city district schools. They do it because they have families who support their education and because they’re in schools that operate without the bureaucratic and union-forced nonsense that cripples traditional schools. They’re not for every kid, but for those lucky enough to get in and driven enough to succeed, most of them minorities from rougher-than-average neighborhoods, they’re a godsend. And the regular schools should be learning from their innovations, not rejecting them.

Hochul wants to expand the number of charters. Many lawmakers do not. She has to stand her ground.

What about the horse-trading that goes into crafting the state budget? Yes, the governor has to make some concessions to secure the victories she needs. We suggest two right away. She could drop her housing plan, which, for all its benefits, would take away too much local control of zoning. She could also accept a hike in bottle deposits to 10 cents and expansion of the drinks to which they apply. Many enviros had hoped that would be in her budget plan and it was not.

Now let’s see Hochul, as steely as promised, negotiate.