So have been there, done that! Here's my advice, after 3 kids...
1. Ditch the diaper changing table. Although it's easier for you, it's a falling hazard. If you NEED to have an elevated surface, use a pack n play with the bassinet top. At least it has higher edges and much less likely chance of them rolling off.
2. We used a blanket on the floor. (Use up those receiving blankets you thought you were done with as a "pad". They are easy to resuse and wash any poop or germs off of.) Or you can also use one of those changing pads that is bucketed. It's a big foam pad that you probably already have on your changing table.
3. Keep diapers, wipes, etc. in a basket nearby. That way you can pick it up and move it if you child wants to tear it apart, yet still have it handy when you need supplies.
4. If you are using a certain area...table, stand, pack n play or blanket on the floor keep a musical toy or posterboard with pictures on it. We used a Fisher Price "radio" that sang songs. The kids loved playing "row row your boat" or "ABCDEFG...". Also we take pictures of our "friends" and paste them onto posterboard and leave it on the wall near where we change. We "quiz" the kids on "Who's that?" For older kids they love to see pictures of themselves. You can show them "baby Nina", "Nina at Christmas", etc or use pictures of family, "Where's Grandma?" You get the idea. It works like magic.
5. If diaper changes are a REAL hassle. Reward them for sitting still. ONE M&M goes a long way towards saving your sanity...esp with active toddlers. If they don't behave they don't get one. Period. We used an old pill bottle, decorated a piece of paper to make a new label that said, "Nina's Potty Treats". (That way they NEVER try to open other pill bottles that have a similar label.) The pill/vitamin bottles usually have safety caps too. So even if she found the bottle, she could never open it herself. (We used ours for successful pee pee on the potty.)
6. Start teaching the word NO or Not Nice. Fighting can't be acceptable. A firm NO while restraining their twisting legs, kicking feet, etc. also paves the way for teaching that it is not OK to kick Mom.