If required mods for Toys&Love, or your content mod, are not installed correctly... animation scenes will freeze, not start, or CTD. Ensure your installation is correct by following these steps.
If during these steps, you make changes to your mod load order or add/remove mods, make sure you are starting a new game. Why?... see golden rule.
FNIS Generate: Use Generate FNIS for Users and Update FNIS Behavior - make sure you see "Toys" listed in the list of Mods that it processes and that there are no errors. A common FNIS error is when you exceed the maximum animations. You MUST Update FNIS Behavior again each time any mod that uses FNIS is added, removed, or updated.
Corrupt Save?: Confirm that your problem is not a corrupt save (see golden rule), by starting a new game, and running the Installation Test below. If the test fails when loading your save, but passes when you start a new game, this proves your save is corrupt.
Requirements: Verify all the requirements listed under the download page Requirements section are met, including requirements of the required mods. Common mistakes:
Not having the correct version of supporting mods for your version of Skyrim. see... SE versus AE Version Trap
Missed or incorrect version of JContainers
Missed installation of XP32 Maximum Skeleton Extended. It's a body mod requirement
If using LE... make sure you have HDT Physics Extensions
If using SE/AE... ensure you've installed the requirements for your selected body. See this FAQ for the bodies.
Sort Order: Use Loot, a tool for sorting mod load order. Loot is built into mod managers and could be already taken care of. Do not re-sort your mods mid-play-through (see golden rule), this is safe only for a new game.
Installation Test
Use the Run Installation Test option in Toys MCM first tab. If this fails, don't expect much to work, you must correct your installation. The above are the common causes.