Liquid stump killer applied will stop any regrowth but the stumps/roots will remain for sometime. To remove all trace! you would have to remove what may be large roots, these can be dug out or look at the possibility of using a stump grinder? if you have enough access but this can be costly.

What a great pity you have cut this down. You can make elderflower fritters. They are perfectly safe for the children to eat. If you have a Forest school practitioner in your local authority they will be able to advise you. If you go to page two of my photos you will find a photo of these fritters along with other suggestions. Being in a childrens centre I would think the grounds will be fairly safe from pollution so they would definitely be able to be eaten. If you leave the stump it may well regenerate. Itis important for children to understand about food and this is free food. Good luck with the new centre

If you want the whole stump out, contact a tree surgeon - they'll have a man on their team who'll come out with a stump grinder and remove it down to a depth of a foot so you can lay the concrete. It'll cost, but the alternative is to hire a stump grinder, and they're not easy to use and very hard work. The only other option is to take the tree right down to below ground level, deep enough for the concrete to go over the top, drill into the stump with a woodbit and fill the holes with SBK (neat) and cover until the concrete's laid.
As for children eating the flowers, they're edible, as are the berries, but I wouldn't encourage eating them, personally - small children won't know the difference between elderberries and woody nightshade berries, if there were any about, and with so many children, its difficult to keep an eye on precisely what each one is doing.

Elderflower tea is a lovely spring drink too - one flower in a jug with abut a pint of boiling water - perhaps a drop more as its not nice too strong. Let it brew for a few minutes and strain. So if your tree does regenerate, give it a try.
Woody nightshade is unlikely to be confused with elderberry - it twines round hedges and has scarlet berries. It is deadly nightshade that has black berries on a low shrub, but they are quite different and not at all common anyway. I think its very important to teach children about wild plants and what's edible - I came across some small boys a couple of years ago who were afraid to try blackberries - what a shame.

Well you say that, Steragram, easy to tell the difference, but its not true - from a 4 year old's point of view - my son once ate woody nightshade berries thinking they were like blackberries, which grew nearby. 2 days in hospital, but he recovered okay. 4, 5, 6 year olds won't be aware of the difference between a twining climber and a tree, they only notice the glistening, black berries... and I find woody nightshade popping up in many gardens, including my own.