My wife and I have two kids who both loathed changing time. I mean, seriously hated it. My current son (who is just over a year old) will sometimes even start crying as soon as he sees us walking to the changing table. Once he is on the table, it can become an irrational battle to keep him from crawling over the edge of the table.
Alas, there has been a solution that works most of the time-- get him engaged in something that thoroughly consumes his attention. You've obviously noticed a part of this, especially if you are having a second person play with your child while you work.
For my first child, and now my son, we learned that the best thing to do is to put a toy in the kids hand. This is a tougher task than one might think. If you give the kid a toy they've recently played with, you may get 10-20 seconds of distraction time. With quick hands, this could be enough time to get the kid unclothed and un-diapered. At that point, you use one-hand to do the rest of the work, while the other restrains the child.
But, we'd prefer to not have to "restrain" our children, if that is possible. If you can find a toy that the child hasn't played with in a long time, or some form of devices that you usually wouldn't let the child play with, you can significantly extend the distraction time because your kid is fascinated with discovering a newly found item.
One exception to this rule of giving the kid "new items" is to give them a cell phone. My wife and I almost never let our children play with our cell phones. If you are also the type of parent who doesn't share your cell with your children, then this is the checkmate option that works every time.
In my case, I pull out my phone and give it to my boy probably once every couple weeks. These are the days where he is extremely tired & cranky, and starts fighting me before I even get to his bedroom door. As soon as he touches the changing mat, I put the phone in his hand and, bam!, instant silence.
I hope these suggestions help. Your daughter will have a unique personality of her own, so she may prefer other types of distractions. Still, if you can give her something to do with her own hands, you can extend the distraction time significantly. Variety is what makes this work, so learn to continually rotate in-and-out new things for your child to "fiddle" with.