I hate to tell you that if trading Pokemon between your own games was the only purpose of a new switch for Christmas, it was completely unnecessary.
When you connect to Pokemon Home on your Switch, and click on the "Pokemon" section that gives you the interface of all your games, there is a button above your games that shows your account and profile picture. If you click on that button, you can switch to a different account that is on your Nintendo Switch, and when placing Pokemon in the default "Home" box, those Pokemon can be placed in any account's game of your choosing.
To answer your question, you cannot directly trade between 1 game card on two switches, as you need two game cartridges from the same pair to conduct trades. Forgive me if this is wrong, but I believe you could receive a Virtual Game Card from someone else who has the opposite game as you, trade your legendary Pokemon to that game, switch accounts, and trade them back.
If you need more help, let me know and I will see what assistance I can bring.