A very interesting question, Hagit! Never thought about it before.
Yes, Kay could have lied about a miscarriage and told Michael it was an abortion to hurt him and to underscore her resolve. But I think that after the Tahoe shooting, she had enough resolve already to have the abortion. Look closely at the look she gives Michael after the shooting, when she's sitting with the children. If looks could kill...so she killed Michael's son "because all this must stop!"