Sykes Try The Old Parsonage Hotel - 01865 310210 no pool but does offer babysitting and is walkable to city centre. Check re. parking though.
Forget the Randolph - my mum stayed there this Christmas and it's tatty and has bad service.
The Oxford Hotel is at the end of the Woodstock Road (city centre c. 3 miles). It looks like one of those hotels that cater for corporate functions, but it does have a pool etc. Don't know about babysitting - ask them to send a brochure - 489988. This would be my last choice as it's a bit too chainy for me.
Might be worth giving The Old Bank Hotel a ring on 799599. This was a former bank which was done up to quite a high standard about a year ago, so they're probably still keen as mustard. Bang in the city centre too. Would suit your luxury criteria but again you'd have to check on their child-friendliness.
Lastly, Studley Priory Hotel ((www.studleylodge.co.uk). This is a few miles out of Oxford if out of Oxford is what you want. We spent our wedding night there before heading off on honeymoon, so can't remember an awful lot about the finer details (winey haze) but it was very nice.
Good luck - post again if you've have need any specific info.
By the way, what did you think of the luxury family hotels? We stayed in the one in Bradford on Avon and were bitterly disappointed. Shabby, rank service and I couldn't forgive the owners of these four hotels for dumping a dog at each one to give it a cosy feeling.