Why dont you sit them down, talk to them about what they will need the money for later on (house deposit?) and then get them to open a stocks and shares ISA each, that you drip feed the money into monthly.
Get them to think of it as a long term investment from Day 1, get them involved by choosing a small no of funds to put the money into. Drip feeding should iron out peaks and troughs of stock market.
Yes, they can still access it BUT if done through one of the fund supermarkets, its not like producing a book at a bank and asking to withdraw x amount. They have to make the effort to decide how much of a fund to sell, and with the right attitude to the money upfront, hopefully wont do that.
Both my DC have inherited (directly, from a cousin of mine) almost 6 figures. From the day we knew they had some money coming (they were 17 and almost 15 at time) we started to talk about how lucky they were, how it would help them etc. Once they got a probate summary and we knew the potential amount, we stepped up the talking, this is your house deposit, you are both so very lucky etc. (The inheritance was unexpected - although my cousin, a bachelor had indicated maybe leaving his money to cousins children, it was by no means certain and no one in family knew extent of his wealth).
DS got his just after his 18th and has been drip feeding it monthly into his S&S ISA, with the remainder in fixed term bonds ready for the upcoming years. If anything, the money has enabled him to become more financially astute at a young age, researching funds and looking at bond rates with me.
DD is almost 17, we got control of her money from solicitors 6mths ago, so we doing same, although its a much lower limit in Junior ISA. On her 18th next year, she will have full control of all money but will hopefully follow our guidance and do the same as DS is doing.
I think a lot is made these days of young people not being able to control their spending, but maybe they need to be helped along the road to keeping savings and investments when they are lucky to have them?