Thanks everyone for all the replies. Sorry I abandoned the thread - have spent the weekend throwing up...

It seems that I caught the sickness bug going around my little ones school..Which may also explain why I was so tired and unable to cope with the mud on Friday...
However, you have given me much to think about and consider.
Summerdays - yes, have found every conceivable route between here and the school, plus a few inconceivable ones....and the muddy one is still the best option, but thanks for the idea anyway.
Purplepolly - It seems I have been forced to take your advice whether I wanted to or not! Today I have given in and let Daddy take daughter and my bike to school. And apparently, he says it's "do-able"

. So obviously all the mud has been washed away by the rain last night...yep that'll be it... Thanks for reminding me that sometimes it's ok to admit defeat. Temporarily...
Origamist - Ta for that. Am off to check out those tyres as soon as I finish this post..
ed_o_brain - Wow - thanks for such a detailed post. My tyres are at 60 psi and my daughter is 5 years old.
We looked at the trailer option when we first decided to bike her to school, and borrowed one to try it out. Sadly there was no way it could be done - lots of the route is just too narrow. Added to that was sprogs reluctance to be in trailer in the first place. She's been thrown onto bikes from very young age, and is used to being up where the action is - usually in front of Dad on his top tube. (
which I just read in Bent Mikeys report as being particularly dangerous!)
Also another problem with trailers or anything longer than my mtb, is that the island at the crossing point isn't big enough for anything longer than a mtb. Daughters dad has an extracycle which overhangs both sides if he gets stuck on the island, which is a frequent event, because the road is so busy.
If I took the main road route to avoid mud altogether,I would have to travel on a 70 mph dual carriage way for 2 miles, and then either ride around a roundabout at rush hour to turn off right, or somehow cross 4 lanes of seriously fast traffic with bike trailer and strongwilled 5 year old.
I agree with you about trailers in general being pretty safe though (if i could trust her to stay put), and would have loved to have a trailer, but I'm not having any more kids so that's not going to happen.
As to sprog walking - absolutely.She is a brilliant kid and never ever complains about how she gets to school:it is very much a team effort with her hopping on and off as required. It's just that on Friday she seemed to spend nearly all her time walking, which seemed a bit harsh!
The seat I have is a Bobike Junior - very minamilist, folds flat when she's not on it, but is sturdy enough to take a child of her age, and allows her to move with me and the bike, instead of being held rigid behind me, which would be odd.
And yes, you are right. There is no shame in walking. Ah well-there goes my reputation..
Silverbow - thank you for keeping the thread going whilst I was ill! I'm glad that you could make use of the trailer info.
BentMikey - Thanks for posting the article. Most interesting.
So many thanks folk. Am taking a couple of days off to think about the school run and hopefully will be able to improve things - tyres etc and make it do-able once again.