Can't do online play between (specifically) two consoles that are game sharing

Set the second console as the "home console" and your good to go.

The account with the Gold subscription will have to be the one that purchased the games and will have to be set as one of the console's home xbox and then it will have to be logged into the other one.

Xbox Live Gold Sharing

Using Xbox Live Gold sharing features on Xbox One

Overview

Here’s how Xbox Live Gold subscribers can extend their Gold subscription benefits to multiplayer gaming, Game DVR, and Smart Match.

• At home: Set up your Xbox One console at home so that anyone who uses it can enjoy multiplayer gaming, even if you’re not home or signed in to the console. Simply designate your Xbox One console as your home Xbox. See
  
  How to designate an Xbox One console as your home Xbox to find out how.
• On the go: Sign in at a friend’s house, where everyone can enjoy multiplayer gaming while you’re signed in.
  

At home with Xbox One

As an Xbox Live Gold subscriber, you can share the benefits of Xbox Live Gold with others while they’re using your Xbox One console in your home. Friends and family can simply create their own account and gamertag on the console, which gives them the ability
to enjoy Xbox Live online multiplayer gaming.

Friends or family members with their own gamertags coming over to play? No problem. They can sign in and play online multiplayer games, even if you sign off.

At a friend’s house with Xbox One

When you go to a friend’s house, you’ll be able to play multiplayer games on their Xbox One console, even if your friend is not an Xbox Live Gold subscriber. Once you sign in with your Xbox Live Gold account, everyone using that console can access multiplayer
games for as long as you’re signed in.

What Home Gold means for the Xbox One experience

With Xbox One, everyone in your home has a personalized account to enable powerful and personal experiences. That’s one of the reasons we created Home Gold. It means that your account and your gamertag are truly yours. You don’t have to share your gamertag
for multiplayer gaming with others in your home, or have recommendations for your children appear next to recommendations for the adults in the family. It also means you can introduce new games to and enjoy multiplayer games with visiting friends. When you
buy one Xbox Live Gold subscription, multiple people can enjoy the best benefits of Xbox Live Gold on your Xbox One at no additional charge.

In short, yes it's possible and it's easy to do. Set the console that your kids will use as your profile's "Home Console", they will be able to play all of your games and use your Xbox Live Gold benefits. You will be able to play on the other console as
long as you are signed into your Xbox Live account and connected to Xbox Live. You will be able to play multiplayer games together at the same time as well.

You can learn about home Xbox here: https://support.xbox.com/en-GB/games/game-setup/my-home-xbox