Well, as you said, you do have control over the situation. Arguing in front of children is NEVER a good idea. It makes children nervous and can lead to other problems. Anyone who came to my house and argued in front of my child was asked to leave; if I was somewhere else and arguing went on, I was the one who opted to leave.
It seems to me that you can lay down ground rules that you will not allow their arguing in your home in the future. Be kind but be firm - start arguing and it's time to leave.
As for the early bird and the night owl routine, I would say either ask your mom to leave by 8:30 or 9 pm, when your dad wants to go back to the hotel, OR tell dad to go ahead and leave and you or your husband will give mom a ride back to the hotel later.
Another alternative is to have a "sleepover" with mom, while dad goes back to the hotel. Once in a while it might be nice to have a "girl's night" with just your mom, especially if you two have some quiet time after the kids have gone to bed.
It's very stressful to be around people who fight and bicker constantly; I know from my own personal experience with my parents. It sounds like it's well nigh time you took a stand and set the ground rules with them. They may not like it at first, but if they want to spend time with you and the kids, they'll come to respect it once they see that you're serious.
Good luck!