I'm in a slightly similar situaiton in that my ex has now remarried and had children with her current man. She has however approached me about changing my daughters surname to that of her new husband ( I should point out that they now live in Germany so their surname does stand out like a sore thumb). I was initially very very against this idea as I felt it was taking away part of who they actually are for the sake of convenience to herself.
However having spoken in depth to my elder daughter about it ( whose 11, the littler one is nearly three so really doesn't have an opinion on the subject yet) I feel now that it's really not my call to decide one way or the other, so I have told my elder daughter that whatever she's happy with, I'm happy with, but that nothing will ever stop me being her father if she needs me.
I understand that the name change is what she wants to go ahead with for her own reasons and I'm going to grant my permission for that.(It's quite complex as you can't change your name in Germany, it has to be done back here).
I can understand why you feel the way that you do. I'm still less than happy about it myself, however if your kids are old enough to know their own minds on the subject I think you should talk to them and see how they feel. Tell them you'd love them to have your name and explain why without getting into a blame game about their Mum etc.
If you really really can't face the prospect of them having a different name to you, or if they are very little and maybe haven't formed an opinion on the subject, then by all means get some legal advice, as I think it's so complex you probably need some, but make sure you're doing it for the right reasons and not just to ' pay her back' for her previous presumptious behaviour.