You CAN add the Always Welcome trait to toddlers, but you have to use a cheat to do it.
With the toddler selected as the active sim, open the cheat console (Ctrl+Shift+C), activate testing cheats by typing testingcheats on, and enter traits.equip_trait AlwaysWelcome.
If that doesn't work, try traits.equip_trait trait_AlwaysWelcome
If you have the UI Cheats mod, you might be able to do this through the UI by shift clicking the sim and choosing "Cheat Sim Info" and then "Add Trait" from the pie menu. I was able to add Always Welcome to my toddlers through the UI, but I'm not sure if it was the UI Cheats mod or one of the trait mods I use that allowed me to do it. (Too many mods. The struggle is real.) :p
Either way, using the cheat codes I included above should work.
I've added the Always Welcome trait to all my toddlers (and all members of my active family) in the game, because my active family often goes to grandma's house (where they grew up) to visit and will stay in the guest rooms for a few days, especially around Winterfest, Harvestfest, etc.
Always Welcome prevents any issues from arising when they sleep over, cook a meal, etc. during overnight or extended stays. Works like a charm. :)
EDIT: The best solution, if you're not opposed to using mods, would be Bienchen's "morewelcome" mod. It completely solves this issue and works beautifully. It specifically "protects" toddler behavior (including sleeping) so that it is never seen as inappropriate. Highly recommend it!
Either the cheats referenced above or Bienchen's mod will solve the problem. I used the cheats before I found Bienchen's mod, but I recommend the mod as the best solution because it makes the whole process easier and applies to all toddlers in the game. With the "morewelcome" mod installed, no one will ever fuss at a toddler for sleeping again, because who does that, right?!?!
Happy Simming! :)