Hard to know without actually knowing how her behavior is. Things can be nipped quickly, so the fact that he's dealing with it may frustrate him.
My husband and I agreed on our parenting style after seeing how kids of friends and family turned out. We started our family late. It was APPARENT to us what worked and what didn't. So we both agree with nipping things firmly right up front with no drama.
My husband is gone 8-10 months out of the year, its' usually me home with 3 under 5, but I always let him get right in there when he gets home and be the boss. He jumps right in if they're not listening to me, and I do the same for him. No good cop bad cop. I don't want the kids to defer to me as the softy. They need the SAME message from both parents, and he doesn't have to make up for lost time when he's home since I'm the strict one when he's gone.
If your connection is working, your husband wouldn't have bad behavior to deal with. BUT, he should NEVER be working from a place of being agitated and impatient. You BOTH need a methodical, calm, firm system that is the SAME. This makes it much easier on kids to learn quickly. If you're standing your ground, and he's standing his, and both people are different, and one isn't home very much, there will be chaos and your husband will feel powerless. Try to get on the same page with him. Be honest with yourself if the behavior isn't what it should be, and ask him to compromise with you. It may help to find a book you can both agree on. If it's a discipline one, or a positive parenting one, whatever, as long as you are BOTH OK with the theory and outcome. If a book is making his blood boil because it obviously won't produce good behavior, you can't insist on using it. Our favorite is Back to Basics Discipline by Janet Campbell Matson. It's not an anti discipline book (tons of those out there), and is practical and real and in alignment with how we were raised, and we were expected to behave well as kids, and did. He may like it if you approve. If the rules are all just "coming from you" he can accuse you of not knowing what you are doing, especially if he sees behavior snowballing. So get a book as back up.
The best way to prevent anger and excessive discipline is to have effective discipline and good behavior.