I think posters have made quite a few assumptions about the father from the OP. He lives 100s of miles away, but the OP hasn't specified whether this is because he moved away / because she moved away / because they both moved away from where they lived as a couple. If the OP had, for example, moved their kids to the other end of the country to be with a new man, then it may cast dad's involvement in their lives in a slightly different light.
I think this is a complex one. Whether the OP is BU depends initially on her reasons for wanting to get the children christened. Do you practice Christianity? Do you attend church regularly?
If not, christening children because it's "the done thing" is a load of bollocks - if it's for that reason YWBU to do it. Moreso where it's against their father's wishes, but that would depend on the true nature of his relationship with the children.
If you are practicing Christians and the children are keen, and if dad genuinely and voluntarily has little to do with their upbringing, I think it would be reasonable for you to have them christened.
I do agree that at 7 the children should have a say. You've only cited RE lessons when it comes to their opinion on this? If this is the extent of their interest in Christianity then it's fairly flimsy. They will also likely learn about Islam and Judaism in RE lessons - are you going to have similar ceremonies in each faith?
Difficult one to call without further info.