The duality of dialog state. How to force the bot to check updates only in the child ConversationHandler?

I have a problem with ConversationHandler, that may come from the fact that I haven't understand very well how to use it. I use parent and child ConversationHandlers in PTB like this:

...child_conv_handler = ConversationHandler(entry_points=[CommandHandler("start_child", start_child_func)],states={    CHILD_STATE:  [        CommandHandler("search", search),        CommandHandler("add", add),        CommandHandler("exit", exit),    ],},fallbacks=[MessageHandler(filters.TEXT, fallback_message),],)parent_conv_handler = ConversationHandler(entry_points=[CommandHandler("start_parent", start_parent_func)],states={    PARENT_STATE:  [        CommandHandler("stats", stats),        child_conv_handler,    ],},fallbacks=[CommandHandler("stop", stop)],)application.add_handler(parent_conv_handler)application.run_polling(allowed_updates=Update.ALL_TYPES)

I make following actions:

1. sent /start_parent to start parent ConversationHandler;
2. start_parent_func callback function returns dialog state PARENT_STATE;
3. sent /start_child to start child ConversationHandler;
4. start_child_func callback function returns dialog state CHILD_STATE;

(attention!)

5. sent /stats command and CommandHandler("stats", stats) triggered (stats callback function does its job!).

Its look like all updates firstly checks by handlers from PARENT_STATE. That mean BOT is in two states simultaneously PARENT_STATE and CHILD_STATE. For some reason PARENT_STATE has priority. But i need to CHILD_STATE has priority and checked first.

Yes i can place children_conv_handler in this example first on the list and get result which i want (trigger MessageHandler(filters.TEXT, fallback_message)), but what if i need two child_conv_handler1 and child_conv_handler2? In this case i don't know what to do. How make CHILD_STATE be the main state or how to put parent_conv_handler into some type of "dead end state" while child_conv_handler starts?

UPD1:Example with two child ConversationHandlers:

...child_conv_handler1 = ConversationHandler(entry_points=[CommandHandler("start_child1", start_child_func1)],states={    CHILD_STATE1:  [        CommandHandler("stats", child_stats1),    ],},fallbacks=[MessageHandler(filters.TEXT, fallback_message),],)child_conv_handler2 = ConversationHandler(entry_points=[CommandHandler("start_child2", start_child_func2)],states={    CHILD_STATE2:  [        CommandHandler("stats", child_stats2),    ],},fallbacks=[MessageHandler(filters.TEXT, fallback_message),],)parent_conv_handler = ConversationHandler(entry_points=[CommandHandler("start_parent", start_parent_func)],states={    PARENT_STATE:  [        CommandHandler("stats", parent_stats),        child_conv_handler1,        child_conv_handler2    ],},fallbacks=[CommandHandler("stop", stop)],)application.add_handler(parent_conv_handler)application.run_polling(allowed_updates=Update.ALL_TYPES)