I just got divorced from my second husband and have his last name. I now want to hyphinate my first husbands last name with it.

You can change your name without any of your ex's authorization. As for your kids, their father's do have a say so. If they object, you'll have to get an order from a judge. The process to change both your name and your kid's is described here: http://www.courts.ca.gov/selfhelp-namechange.htm

In your Petition or Response in the Divorce case, there was an entry which you could have checked, which enabled you to request that the Court restore your former name to ___________; it might or might not be possible for you to seek an amendment of the Divorce Judgment to get the name change, through a Request for Order proceeding. However, there is a proceeding available to you for a name change through the Civil (as opposed to Family Law) Court.

Check Form FL-395, a restoration of former name after entry of Judgement of dissolution. It should also work to request to hyphenate your name after the judgement has been entered. Good luck!