It’s worth contacting his employers separately because he may have other benefits that are triggered if he dies while working for them, particularly if it’s a big company. If you’re young like your dh you may well not really think about them or tell your partner about them as you never think that you’re going to need them...
For example, dh’s Company and several others I have worked for have a payout if you die while employed that’s maybe 1x, 2x, 3x or ? of annual salary that’s in addition to life insurance. There’s also an annual amount per child that gets paid to the mother to help with living costs - think for dh it is until each child is 18 or leaves full time education. There may be more or he might not have had any of these but it’s really worth checking, particularly the one that pays money every year, which could really help to ease the pressure on you.
Regardless of what your dh’s will says (eg if he left it to his parents or the local cats home) I understand that if he has dependents and doesn’t leave anything for them then they have the right to go to court and get some assets to help.
Do you have legal insurance? (From your house or car insurance, bank account, your own work, union, even maybe your ex’s work etc). Definitely worth speaking to them (it’s free!) to find out what your rights are.
Do you know if he had a Will? If so - who the executor is and what’s happening? Or if there is no will - and he died intestate then that still leaves you as his next of kin as his wife and there are laws about how the estate should be split up. But it’s pretty shocking that your in laws have managed to get money before his own children, particularly if you’ve had no communication from his scheme.
How organised was your ex? Did you have a Will when you were together? Is he the sort that would have raced off to change it (and update work nomination forms etc) the moment you split or would he have put it on his list of jobs to do one day that would have taken him a while to get to. Particularly if it’s the latter you may find that if you both had wills that his would be the most recent he had so worth checking.
Sorry a post with lots of things for you to check on at a time when you are already incredibly busy but doing so could provide massive benefits to you and your dc.
And on a completely separate note, if your ILs are managing / controlling money that should be for your dc then I hope that they are going to provide accounts and receipts too. And not use money for holidays for themselves to take the dc on rather than you. As for schooling, start asking for uniform money, including shoes, whenever you need it - price it out in advance so you can say that you need xyz items at n cost for their schooling, likewise school trips, swimming lessons, school clubs or equipment etc. Then when they pay for those things you can point out that they are not helping with those things and it’s the day to day expenditure that needs helping with first before luxuries. Good luck!