For the following paragraph I'll ignore, for the moment, the fact that you've got Sky:
It seems that your DVD/Video Recorder only has an analogue tuner inside it, which used to feed its output to a DVD. That tuner is now redundant. The only way you can use your DVD recorder for recording Freeview is to feed a signal from your digital TV (or Freeview box, as appropriate), via a Scart lead, into the recorder. (i.e. you'll be replacing the recorder's useless analogue tuner with the digital one inside your TV or Freeview box). However that means that you'll only be able to record what you're watching.
Now I'll add Sky back into things:
If you've got a digital TV (rather than an analogue TV with a Freeview box), you still won't be able to record one signal while watching the other. However if you've got a Freeview box (with either an analogue or digital TV), you could feed the Sky signal to the TV (as if your recorder and Freeview box didn't exist). But you could then use the Freeview box to feed a signal, via a Scart cable, to your recorder. You'd then be able to watch Sky while recording Freeview.
Any attempt to use your recorder (as in either method above) requires that you must set the recorder to record from 'AV', rather than from any numbered channel. (Some recorders might label 'AV' as 'Ext', 'Aux', 'Line', 'Line In' or similar).
Chris