I would definitely wait until all indications of the false pregnancy are over to spay.
Yes, they do spay dogs that are in heat, and dogs that are pregnant, but it is not ideal. It makes the surgery more complicated and more dangerous. If you are thinking this is totally hormonal, then it is best to wait for the hormones to settle naturally and then spay.
Good luck. I would think getting her into training as soon as she has recovered from the spay would be your best bet.
Jenna, RN CGC & Babs, CD RA CGC HIC
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Dolly CGC & Bear CGC