Thanks for reaching out!
There are two options for a hitch mounted bike rack: 'tray style' where the wheels of your bike sit in a 'tray' and are secured with a strap on the back wheel and an arm bar to the front, or a 'hanging style' rack where the 'arms' of the rack go through the frame of the bike and are secured to the top tube of the bike. A 'hanging style' bike rack can be challenging to use with kids bike (or any bike with a small frame for significantly sloped top tube), depending on how the frame is designed and whether there is room to get the arms of the rack through the frame. Sometimes that issue can be mitigated by using an adapter like the Thule XT Top Tube adapter.
Here are a couple of 'tray style' options that you could consider:
and here are a couple of 'hanging style' options to consider:
Lastly, if you need to get more than 2 bikes on a 'tray style' bike rack you will need to purchase the 'add-on' piece for them:
Hopefully this helps, thanks!
For mountain, I'm definitely all for tray style because of just what @REI-JohnJ said about the sloped top tubes. I've been a big fan of my Saris Superclamp EX4, but it looks like that's not in stock right now, though the two bike version is https://www.rei.com/product/126641/saris-superclamp-ex-2-bike-hitch-rack.
For kids bikes, I've heard it can be hard to fit on any rack if it has 16" wheels. Most racks should fit 20" and up just fine. 12" and 14" bikes for really small kids/toddlers probably just need to go in the trunk.
A final consideration is that if you need to carry more than 2 bikes, you probably also need a 2" hitch receiver, as most racks for 3 and up don't come in a 1.25" version due to the higher tongue weights.