TBH - you could end up losing your nanny if this continues.
At the moment you are apparently paying over the general rate at £6/hr/child
If your CF colleague bungs her kid into the mix, too, then the rate drops to £4.50/hr/child - and she has extra work - and some of this, as a PP has pointed out, will be keeping the peace between children squabbling over sharing toys etc. This isn't like looking after siblings, who quarrel but who know their boundaries. Your children will have an invader in their home and might not like it long term. Your nanny might get fed up, and find another job which might pay a bit less, but would be less stress for her.
I was also a bit struck by these comments you made, OP
Personally I don't think it is unreasonable to discuss how we would split the payment but lots of people on here seem to think it is.
I disagree. Your nanny has contracted with YOU to look after THREE children for a particular rate. It is not up to you to decide to add to her workload for no extra payment.
Actually she did make a very fair point, my dd is not really in the nanny's care because she is in school/ after club so her dc is like a replacement.
So why are you paying for the third child at all? Because she is part of the arrangement you and your nanny agreed. Her DC is not "like a replacement" at all - otherwise she would be instead of your child for the same hours as your child.
Would your colleague agree to take on 33% extra duties at work, having to fit them not the same hours, for no increase in wage? I'll bet she wouldn't!
If anything, your Nanny should charge more than £6/hr for this extra child if she decides to take her on. Generally people looking after children charge £x for the first and then £(x-y,) for siblings. Brothers and sisters are at a slightly cheaper rate. But the first child of another family would be back to your higher first child rate.
And what happens if her child (or yours) is ill (infectiously), and needs to be quarantined? Who gets the nanny's attention. What if your colleague decides to work extra hours, or fancies an extra day off work to go shopping and wants her child looked after for a few extra hours in your time? What about trips to the park, playgroups etc - that's a lot of children to take care of. And the safety aspect has to be considered.