Can separation anxiety be accompanied with anger and frustration when my husband leaves the state to visit his family?

Yes: If these are reactions to your husband leaving then the answer is yes. Distress and upset in response to events stem from the way you're thinking about the situation, the implications, the fairness of it, what this means to you, etc. Being upset at your husband leaving is not directly related to his leaving, per se. It's caused by interpretations, which can at times be exaggerated.

Certainly: Especially if this is a repetition of earlier traumatic separations from primary caregivers. I commonly see patients with attachment trauma struggle to be left even when intellectually they know there is no threat to the relationship. Psychotherapy can help you unravel these feelings.

Yes: If you are feeling abandoned this will likely lead to anger and frustration. Ask yourself if this reaction is realistic or coming from past hurts that don't belong in your marriage.