The bikes are the first thing on the list that nobody thinks about until a Saturday morning, when the kids want to ride to the park at Mom's house and the rack is still in the garage at your place. Before you buy anything, you need to know which car will carry the bikes, and whether the rack you pick can go on that car without a fight.
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Start with the car that does the hauling
Walk out to the vehicle that will carry the bikes most often and write down three things. First, whether it has a hitch receiver, and if so, the size of the opening. The size is usually stamped on the receiver or listed in the owner's manual, so look there instead of guessing. Second, whether the rear hatch or trunk lid opens wide enough to load a bike past the rack. Third, whether the taillights and license plate can still be seen with a loaded rack on the back. Those three answers will rule out more racks than any product page will.
Do the same walk-around at the other house. If Mom's car is older, lower, or has a different hitch, the rack that fits your car may not fit hers. Write both answers next to each other on the same sheet. That sheet is what you bring to the store or the website, not your memory of what the car looked like last spring.
Measure the bikes, not the kids
Bikes come in more wheel sizes and frame shapes than most parents expect. Measure the tire width and the distance between the wheel centers on the bike that is largest in the house, since that is the bike that has to fit. Check the frame too, especially if one kid has a step-through frame and the other has a bar that runs straight across. Some racks hold the bike by the wheel, some by the frame, and some by the seat post, and each one grips a different shape. If you have a bike with a basket, a child seat, or a trailer hitch of its own, add those to the list, because they change the load and the swing.
Look up the rated weight of the rack and add the weight of the heaviest bike to it. Then add a little room for the bike that will get a new seat or a bigger basket next year. The rack's rated weight is on the label or in the manual, and it is the number you compare, not the one on the box.
Decide who moves the rack
Here is the part that decides whether this works for a split week. A rack that comes off in ten seconds can move between cars. A rack that needs a wrench and a level stays on one car, and the bikes go wherever that car goes. Decide which one you need before you buy, because the choice shapes everything else.
If the rack stays on one car, name the adult who loads it and the adult who checks the straps before each trip. If it moves, name who carries it between houses and where it lives when it is not on a vehicle. Write those names on the same sheet as the measurements. A rack that sits in the wrong garage on the wrong weekend is just a very expensive shelf.
Before the first trip
Mount the rack in your driveway, not on the road. Load the heaviest bike, tighten everything, and then open and close the hatch or trunk. Pull on the bike with both hands and look at the contact points where the rack touches the car. Check that the lights still show and that the plate is clear. Then drive around the block once and stop to look again. If anything shifts, fix it before the kids are in the back seat, not after.
Once you have done that, you will know more about your rack than anyone at the store could tell you. That is the whole point of measuring first. You are not trying to get the perfect rack. You are trying to get the one that fits both cars, both hitches, and both bikes, and that a grown-up in each house can actually use on a Saturday morning.