Enforced naps and crate training

Hi everyone!

I’ve got a toy poodle here - 10 weeks old. She’s the sweetest little thing but can absolutely be a menace - whining, biting, chasing the cat, you name it. She’s really good with the crate at night (we’ve got it beside our bed) but she refuses to go in during the day. We give her all her meals in the crate and she’ll even jump in every now and then when she’s playing with her toys. She loves naps and I never have to enforce them on her. The only thing is she ALWAYS wants to nap on the couch with me and if I’m not on the couch, she’ll come and nap at my feet. If I move her into her crate after she’s fallen asleep, she’ll wake up and walk right back out and follow me around. I tried closing the crate door and covering it with a blanket - that was HELL. She cried and cried and cried until I let her out and then she fell asleep two seconds at my feet.

My question is - should I be putting her in her crate at all if she naps happily. If I do need to, do I just ignore her crying and hope that she’ll learn to love her crate during the day and will eventually nap in there without making a fuss? Should I go the way of crate games and really stick to it so she gets the idea that crate is good no matter what time of day? I’m terrified that she’s got really bad separation anxiety, but is that normal for a pup her age?