I know you've realised by now, but you're definitely CF. Basic rule of thumb for me, if you're asking is that what you're offering in return should be at least the same amount as what you're asking.
You are asking for her to look after your toddler 9-1 ie 4 hours which includes feeding lunch and taking them to nursery. Adding an extra toddler is not like adding a school friend, which can entertain your child. It's another child to entertain, to take to the toilet/change nappies, wrestle into the car etc. It adds complication to your dc rather than making them easier.
In return you were offering picking their dc up from school, which you'd do anyway, and take them to an activity, which you're doing anyway, and then bring them home again, which you're doing anyway. You're not entertaining/feeding them.
So you are basically asking her for a big commitment that you could easily be paying over £100s per week, in return for very little.
And actually I liked picking the dc up from school, hearing what they'd done etc, and my dc would not have appreciated not being picked up 4 days a week.
Offering to help means saying "My childminder's ill, could you take them today." or "I've got a dentist appointment first thing and I need to leave half an hour earlier, would you mind taking dc to school" not an every day thing.
I'd backtrack very quickly, or you'll have lost her as an emergency call, because she'll wonder if she agrees whether you'll push for more.
And those who are saying that's just till Christmas. Well, other than the possibility of the person turning round and saying "well, it was going so well, I was assuming we'd continue", that's not a short length of time. It's 2 months. And December they may well have Christmas plays in the morning-taking 2 toddlers along to that won't be fun, want to do Christmas shopping (not too hard with 1 in the buggy)etc.