If scoped to the Y, the vehicle already has native access to Superchargers and a NACS (Tesla) charge port, so this is the best situation. They should've been given a J1772 adapter at purchase, if not, you can pick them up cheap on ebay or Facebook Marketplace. I recommend it for opportunistic level 2 charging on older stations that have not yet upgraded to the NACS charge cable. If renting, ensure the vehicle has access to Tesla's Superchargers; traveling without them will be a suboptimal experience, and take much longer.

https://shop.tesla.com/product/sae-j1772-charging-adapter

If kids are with you, do your best to preplan which Superchargers (or other fast chargers, Electrify America perhaps) you're going to hit on your route. They're on the map, so it should only take 30-60 minutes to zoom in on your map provider of choice to see what is available near each charger. Optimize for amenities nearby that are kid friendly. There are great locations (24 hour bathrooms and food, activities, venues) and there are not so good locations (I've charged at midnight behind a dead mall in rural Missouri, I would not recommend such locations when traveling with family members).

https://teslamotorsclub.com/tmc/threads/superchagers-near-pl... might be of help, there are other threads on the forum that will provide additional kid friendly context.

Charge time will be between 10-25 minutes in most cases. The newer the revision of Supercharger (V1->V4), the more current you'll get, but this is only relevant if the vehicle battery state of charge is closer to 0% (due to battery management and charging dynamics). Avoid V1 Superchargers when possible, as they max out at 150kw (this info will be available both on supercharge.info and within the vehicle's navigation system). TLDR Empty batteries charge faster, don't charge beyond 80-90% unless the last fast DC charge of your day's journey (the last bit of the charge is the slowest).

If you're traveling somewhere "off the grid" with limited fast DC charging options, have the mobile connector unit with you with plugs that will be most available (https://shop.tesla.com/product/mobile-connector). You can gain ~48 miles of range per twelve hours charging on a 15A/120V circuit in a Model Y (overnight charging).

https://abetterrouteplanner.com/ is a helpful trip planner, it will build your route around desired charger locations, estimated vehicle performance, and state of charge of the vehicle as you travel. You can save your plans to it as well.

Safe travels, and have fun!