I've known enough people who lost cats during a move (they slipped out with the realtor or movers, etc) that I would move the cats first.

We moved our cats with most of their belongings - the litter box, bowls with food and water, and the bed to one of the bathrooms. Put a sign on the door “cats! Don’t open the door” but a few times one of us would stop by to pet them and give them treats. They were just fine. I’m not sure what I would have done with a dog.

I might take them to the family members house because they might slip out or get underfoot while you're moving furniture. So it will be safer for them to be away.

But I have a cat who flops in front of people to be petted a lot (so she can be a bit of a trip hazard).

Just make sure that they have a safe place to hide in the new place. Don't open their crates into an empty room. Make sure there is a bed or something they can hide under.

You are familiar. The chaos isn't, but you're still there. They'll probably be happier where you are. Packing and strangers are medium stressors. Being in a brand-new place, without their familiar people, is a major stressor.

Try to leave a small area as stable as you can (litterbox, food, a few toys and a scratching post of some kind). When you do move the cats, move their "stability items" and such to whatever space will be most stable where you're staying. Same thing when you find permanent housing.

They'll be fine.

We are moving almost 1000 miles away. Our house is under contract but there's a few things with my spouse's job that have to be worked out before we can officially move, so we haven't found a place in our new state yet.
So in a couple weeks we will be "homeless" but we have a family member we can stay with in the meantime.

We've been starting to move a lot of our stuff into a storage unit, and a few other things we've been selling on facebook marketplace or getting rid of. Our cats are pretty confused by all of this. Would it be better to have them stay in the home with us as long as possible, even with all this "chaos" (rooms being packed up and emptied, sometimes random strangers coming in, etc.) Or should we move them to the family members house asap?

For what it's worth, they have never been to this family member's house before and I do not think they will be happy there.