Can I get separated and still have the right for my husband to pay for our children expenses?

First, I am sorry to hear about your current situation. Second, your husband does have a legal obligation to support your children, as you do. In Texas, child support is largely ruled by the Texas Family Code guidelines. If you need assistance establishing child support, a private attorney can help, as can the Texas Attorney General (search "Texas Attorney General child support"). In some cases, legal aid is also available to parties. I would not delay in filing suit, however. Best of luck to you - and keep your chin up. You will get through this.

The best vehicle for this would be a divorce. A divorce will either or on a final or temporary basis provide orders for paying expenses, alimony, and child support. However, if you do not want a divorce you can still ask for orders regarding the children through a lawsuit called a Suit Affecting Parent Child Relationship.