We did the trip last September - great fun. We did Dover-Dunkirk-Calais-Dover over 2 days. Yes, in Calais we had to go in the marina which meant timing departure to get over the sill - but that was OK, the kids were sent to move the rib to the outer harbour and wait while Mum and Dad finished their lunch and digestif...
We were in fact offered fuel in Calais although as we'd filled up in Dunkirk we didn't need it - but it does seem to be available - worth checking, maybe something's changed?
I assume you know about the traffic lanes and crossing them at right angles - we found a handy nav marker was that if you head east or a tad south of that out of Dover you come to a buoy (can't remember the name offhand but look it up on the charts) on the edge of the lanes, go across at right angles to the lanes from there and it brings you to just off Calais
Dodging traffic in the lanes in a rib is so much easier than in a yacht!
Need VHF clearance to leave and enter Dover Port
Calais entrance and departure controlled via a traffic light system (IIRC so was Dunkirk) rather than using VHF
Take all your passports, boat docs etc, although on our trip no-one was interested in looking at any of them
Have a great trip!