Since, as you say, you don’t believe your DH will step up on the parenting and housework front if you work more hours YANBU at all to be frustrated and annoyed at him. He was happy to stretch things and use the money to do what made his life better (moving to a bigger house) but that decision looks set to make your life harder and of course that seems unfair.
But I also think your plan to use the inheritance is unrealistic, too short term and, where it involves “borrowing” money left to your kids, very unreasonable. I can see why your DH and FiL are against it.
A good arts degree and a decade or more out of the workforce leaves you in a very vulnerable situation, financially. As you’ve recently noticed, you aren’t able to walk into a good job. You’re also about to hitting the age at which employers seem to discriminate in hiring (on top of your lack of recent experience, old qualifications and your mother status). From a getting a good job perspective this does not look at all good.
I think you need to stop fixating on how to continue to be a stay at home parent, your family wealth, even with this inheritance does not sound significant enough for that sort of lifestyle.
10 years of supplementing your family income with money from the inheritance won’t even see you through your children’s education and you will have even fewer job prospects at that point. That’s not good planning for you personally or for your family. If your day-to-day expenses were covered by your day-to-day income, your DH might be more in line with the idea the inheritance money can be enjoyed. But really if you want to be sensible for your family, you should use what’s left of DH’s inheritance to invest in increasing your family income to a sustainable, higher level by getting you back into the workforce in a well paying role.
Look at how you can best improve your personal financial prospects and your marriage such that you DH stops treating the family as women’s work he can leave to you. Look into training for a new career, volunteering at a high level that could get you back into the workforce on a high wage or consulting if you still have industry contacts. Try to aim to be earning a reasonable, full time wage by the time your youngest is in secondary. Talk with DH about the additional support the kids (not you - it’s your kids) are going to need if you are putting in more time outside the home. Discuss how your current housework/childcare roles are going to be covered and how much it will cost (including cleaner, increased food bills, holiday care, babysitter at the weekend so you can have equal time off, etc. if he isn’t prepared to do any more than he currently is). If he isn’t receptive, consider marriage counseling, but don’t back down on your improving your work prospects - his selfishness makes your need for good personal financial prospects even greater) This is going to take effort and there may be a lot of pain before you get to the point where it seems reasonable.
Work on your fear of childcare - it has many positive benefits and a fear of it is irrational and doesn’t serve you or your family well - and start using it a bit. Find the types your kids enjoy. Sometimes childcare isn’t great (but some family life isn’t great either) but most of it is positive, especially for kids’ social development.
I don’t think you’re being unreasonable to be annoyed at your DH, but I don’t think you’re being reasonable to cling to your SAHM role.