As I have already said, I have been to countless mosques all over the world both as a tourist and for diplomatic purposes, the women (inlcuding my wife) were ONLY ever required to cover their shoulders down to their ankles and in a very few places cover their hair as well. I am talking world famous and small local mosques here. Similarly I have been to countless cathedrals and churches and Synagogues and Temples of all sorts.
I really don't see any issue with children going to a mosque (or ay other place of worship, maybe dodgey cult ones being an exception!) and I would encourage it. I can see no long term issues with letting a child learn about other cultures - especially when they are invited to do so in that cultures place of worship. It can only broaden their minds. I still debate the whole face covering thing was required, but an element of 'dressing up' in the 'this is how we go to prayer' may even add to the ineterest of the children who participated. I am sorry your child missed out Blyss, but lets hope that she will not grow up being scared of what may or may not go on on the inside of the mosques she walks by, as she has never had the opportunity to see for herself.
I would even encourage children to visit my local place of worship, providing they respect the rules of the place. Which is that they should remain well behaved, should not stand near the bar, must not smoke in the no smoking section and should not play pool if they are under the age of 16 (or something). They should also respect my right to enjoy a pint of old peculiar in relative peace and satisfaction.