I think Cersai really loved at least Joffrey and Myrcella, but I don´t know how she would have acted if they stood in her way to power. And I think she despises Tommen´s "weakness".
We never have all information, so almost always there are more possible interpretations, and I agree that part of Cersei's rage was due to the fact that it was Tyrion who arranged marriage but because of own her bad experience Cersei is more emphatic at least in this situation. In the books Cat thinks that hers and Lysa's marriages are similar before Blackfish tels her otherwise.
About Jaime, I think she let him go because she was desperate after her sons' deaths. Of course she loved her children, but for me it always felt like she made Sophie's choice a little too easily when it come to crossing the Twins. It helped Robb but even Robb tells her that Arya will hate it.