You have had a roasting, OP. The thread has been pretty united in not spending the children's inheritance and your last update seemed to agree.
You do work some paid hours. You have applied to at least a couple of jobs with longer hours and have been unsuccessful and had your confidence knocked a bit. The deceptively simple "get a job" and "up your hours" posts seem to ignore the difficulty of doing those things.
Between your current job and volunteering you should have good references and transferrable skills which is a start. But it isn't easy and it's difficult if your confidence is low or you have a lot of anxiety.
Anxiety. There's a lot of that in your posts. I have experienced it myself and I want you to know that you can get help and it can get better.
I think you and your husband have to take a good long look at the finances. If you managed to get the mortgage then it could be that reducing spending in other areas could be enough to give you space to train or build up your own business so that you could be contributing more in a couple of years time when childcare is less of an issue as they are older.
Some counselling might be helpful to deal with the anxiety around your mother's death. I know where you are coming from, my DH's dad died young so we have a tendency not to want to put off living for family, experiences etc until retirement the way some folk do.
Working on yourself, your anxiety and what kind of career might suit you longer term would be healthy I think.
It's hard when things are tight, not to focus on the possibility of a quick fix. I know that when we are low on funds is when we fantasize most about even a small win of money to solve our problems. It's human, if not entirely sensible.
Lots depends on the specifics of both the inheritance (how much of DH's share remains) and your current outgoings, and what savings you could make. Do work on a detailed budget with your DH and see what your choices are. And decide about more hours at a similar wage in the short term is immediately necessary and/or working on more longer term plan of a career or business for you for when your children are older and what that would look like and what the first steps of that would be.