I was asked to come in 1hr earlier than my shift starts but I can't since I have kids and I was told I will get points for not showing

Employee Handbook

Since you do not have a union rep to help you, you will have to be your own advocate in this scenario. The first step is to check your employee handbook with what it states for work hours and how much notice you must be given for any changes in those work hours and what exceptions it has for overtime. You may get lucky and find something in there that makes this a no go for your manager.

For example it may dictate that you are given one week notice before any changes to expected working hours. If that is the case and your manager gave you only 24 hours notice then you can take it to HR. HR's goal is not to protect you, but the company. Which if the manager is setting the company for a lawsuit from you then they will come down on that manager.

Ask for Help from Coworker

If you have a fellow employee who was not tasked with this, but could do it instead of you as a favor for you. You can take that to your manager and offer that as an alternative solution. Whether or not they accept it would still be out of your control.

Get a Babysitter

If you have extended family that lives near by, neighbors, or friends that you trust to babysit your kids, you can see if they are available to cover for that one hour. As a stop gap/last resort measure you can hire someone to babysit for that one hour that neither you nor your spouse are home for. I do not recommend this solution since it costs money that the business will not reimburse you for, but if you have no other choices this can get you through the immediate problem until a more permanent solution is found.

Your Children Are More Important

At the end of the day remember that jobs are temporary, but children are not. As such when a terrible manager puts you in a situation where you have to choose between work and the wellbeing of your children, the priority is your children.

Yes it's legal

You have a job, not a guaranteed arrival and departure time. It's tough, but certainly not unheard of to need to come in early or stay late.

You should talk to your manager to discuss the hardship, but in the end if you are still forced to come in early you'll need to figure out a solution, as @Anketam recommends. In today's economy, I would not do anything that affected my employment