Hi, lots of good schools in Derby area. The best will be full but you may get lucky. Key thing is to move to catchment of the school you like. Your younger child should then get a space.
Some to consider:
Ecclesbourne in Duffield - excellent school, high attaining, make sure you are in catchment tho (Duffield, surrounding villages but not Milford/Belper, some bits of Derbybitself)
Littleover CS - another excellent school, very good results and atmosphere
Woodlands, newish head, good facilities inc swimming pool, catchment includes city centre
Landau Forte, another good school, no catchment, prioritises certain inner city areas, in city centre so easy to get to, good attainment
Chellaston - bit of a hot house reputation and poor ofsted recently ish, but gets good results
West park in Spondon Aldo worth a look.
I would avoid: merrill (new name now I think), Noel-Baker, Derby Moor. Murray Park ok but not the best.
Some of these schools have no sixth form
Hilton feeds to John Port in Etwall, vvv big school, don't know much about it tho.
Castle D is in Leics so system is different, no knowledge of school there tho.
Also a popular school is George Spencer on the A52.