Investing it for your kids and you being able to get it out are kinda mutually exclusive.
Last advice I got in a similar situation was to stick it in a pension plan (for the kids). Seems weird to be putting money into pensions for kids, but if you think about it logically, it does make sense, £4K now will be worth a lot, lot more when they retire than £4K invested by them in their twenties or thirties.
Although you probably won’t be around to be thanked for doing it!
Best wishes grantus – sounds from what you’re asking like you’re continuing to cope and are on top of things, at least the practical stuff that needs dealing with, hope the other stuff is starting to get a little easier too mate.