Hi Claire and Rob
We live in the North West and travel into Wales quite a lot with our 'van. I'm not sure of the route from Sheffield to M6. Once you reach the M6 take the M56 towards Chester. It is possible to go around Chester on the South or North sides. To go south turn off on the M53 and then that becomes the A55, north Wales express way. The A55 leads all the way to near the Menai Bridge to Anglesey. It becomes the A5 just before the bridge.
Alternately to go the north of Chester go to the end of the M56 and then follow the signs for Queensferry/North Wales and take the A5117,A550 and A594 to join up with the A55 and then the route is as the south of Chester route. Either way around Chester is good and dual carraigeway when not motorway. I just listen to the traffic announcements as I travel down the M56 and choose the best route from that.
All of the A55 is a very high quality road, mainly dual carraigeway and with lovely sea and country view along much of its route. It is an excellent road for towing as it bypasses all the towns and villages enroute. It does, however, get very busy at peak times, eg, Bank Holidays and it the major route for hgv traffic to the boat at Holyhead.
On Anglesey I would recommend Ystad Parc Lodge at Cemaes Bay. It is quite a basic site but has lovely views over the coast and its own small beach and lots of space for your kids and dog to play. The owner Lizzie is a lovely person - she gave me a bottle of wine because I recommended the site to another camper who was looking for a site!! The village of Cemaes Bay has a good range of small shops and pubs and lots of lovely walks.
You can see reviews of the site here
http://www.ukcampsite.co.uk/sites/reviews.asp?revid=1712
UKcampsite is an excellent website too with lots of reviews of sites on Anglesey if you don't fancy Ystad Lodge.
Hope you find somewhere good and have a lovely time.
Tim