I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
If you file for divorce, which you can do on the grounds of abandonment or irreconcilable differences, you'll be able to seek child support to help you continue raising the kids. The judge can order a paternity test at his request, which he'll have to pay for once it turns out that he's the father. But a judge doesn't have any ability to order one spouse to support the other or the children while they're still married - one of them has to file for a divorce. You'll be able to ask for spousal support at the same time, so you can maintain the marital standard of living until you're able to find a job that would allow you to meet your needs (along with child support).
You're also entitled to half of all assets acquired during the marriage. That includes the value of cars, bank accounts, if he bought a house with community property when he left, and things like that. All assets that either one of you obtained during the marriage, other than through an inheritance or gift, belong to both of you and must be split under community property laws.
The state has forms and instructions online that you can use to open a case. You're also allowed to seek temporary support until the case is over, although it may help to have a local attorney help you with that.
You would have the ability to ask a judge to order marriage counseling if your husband opened the divorce first. However, when you've been separated for two years already, it's possible that the judge would say no. But that also leaves you at his mercy, waiting for him to go ahead and file for divorce before you can get any money out of him, and that's not fair to you or your children.
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