The working-single-parent in me is breathing that deep exhale that you have childcare expenses covered like this. What an amazing gift and a way for your wife's grandmother to keep being present to nurture your child even after she passes. That is just a huge pile of stress off your plate.

I got a big sum of like 15k last summer from some work I did, and I was so glad because it gave me some flexibility to make childcare choices that allowed me more time with my son. That sounds kind of confusing to spend more on childcare in order to have more time with your child but it's how things played out for me. For instance, nannies are more $$ but they eliminate the transition time so you have more family time. In my case I was able to purchase the more expensive childcare option that was closer to home, even though I only needed childcare 4-days a week but I had to pay for a full week. Getting my childcare budget addressed allowed me to create more breathing room in my life, not just in my budget.

With 1 and soon to be 2 young kids and 2 working parents I would be thinking about actually increasing your childcare budget if there are ways that doing so could create more breathing room in your life. Or, for instance, creating a budget for someone to clean the house. Just anything that creates more ease and breathing room in a day-to-day way. Maybe extending parental leave by a month. Have you thought about using any of this money to create more time?

in terms of investing all at once versus holding the cash and spending it down, I guess I'd choose your second option - getting all the money into investments sooner not later. However, I'd be holding back more than the bare minimum. 

I assume you have an emergency fund fully funded. 

Another thing to think about is a 529 for each of them. There is lots of controversy over this but where I personally came down was to put 2K in my son's 529 account and then leave it. Over the years this should develop into a small pot of money so that I at least have *something* to offer him for college or vocational training. When my retirement is in an even stronger place than it is now, I can contribute more. But in the meantime that 2k will compound. 

So you might think about sending some small amount to a 529 for each child, a little nest egg. You totally have compounding on your side and if used for education expenses, alllllll of that growth is tax free to withdraw. I understand not going wild with 529s and prioritizing one's own retirement, still at the same time, a large gift like that is maybe a wonderful opportunity to launch some momentum for your kids when they are 18.

Finally, for me personally, no big windfall like that can be budgeted out without some meaningful allocation towards the common good, whether that is environmental/climate so that our children inherit a livable world, food banks to help the people around me feed themselves, the local teen homeless shelter, scientific research and development, or whatever cause is meaningful to you. This is intergenerational wealth so I think, as we experience gratitude towards our own ancestors, that we are mindful to create ourselves into ancestors for our entire community, not only our direct biofamily. That is just my own perspective.

Just some ideas. I'm sorry for your family's loss. What a gift and generosity from her grandmother. Very, very precious inheritance at this time in your family's life.

At the very least use some of the money to max out two Roth IRAs. Roth contributions can be withdrawn at any time, so this should be a priority.

I would not cut back on the retirement savings and if possible I would look for ways to increase it and use the money from the inheritance to cover some of the "lost" income.

I'm so sorry for your family's loss, and I've been in this situation in the last couple of years.  When my mom died in 2019 I mostly inherited IRAs and some stock which stayed in the market, but I got a $200k refund from her care facility.  I took half into my budget and the other half diversified into the market with everything else.

My biggest concern was the payments for my kids' private school at the time.  She had been helping with that in the past, and now it was on me.  I used the inflow to boost a lot of true expenses and top off my income replacement fund.  I put enough into the school tuition category to cover payments for the rest of the school year, and then started to work on building it up again before it was spent down (I used target date spending goals for that).

I *thought* I'd end up spending down all the cash, but our regular income increased and I was able to "slow the bleed" and then reverse it into a net gain, with YNAB's help of course.  So I'd say you guys are still moving into your prime earning years, so don't discount that your budget might have some more wiggle room in the near future.  Since you have known expenditures I'd keep that cash in your budget and keep it safe until you feel your income will support you without it.  I am slowly saving that $100k I put in (well some did go right back out to charitable giving) with a goal to eventually transfer it out to investments, but it's not life or death, just a 5 year goal I'm shooting for and I'm over 30% there.  If I need the money, it's there.

As far as where to physically park it, I have it both in high yield savings and a very conservative income-based intelligent portfolio at Schwab.  It's on budget, but I only record the income and have a buffer for major balance fluctuations (hello March 2020!).  So keep investing the way you are, it sounds like you're doing all the right things.  I posted about this a couple years ago, you could search for my post that was something like "What do I do with all this cash?" where everyone gave me some great ideas.