I am a SAHD and we are in almost exactly the same position, albeit because of an inheritance rather than a gift from a living relative. For background I came to the end of a contract just as DC1 was born so stayed at home while my wife (also a solicitor) went back to work, we had DC2 and I then took on caring responsibilities for another relative who is likely to shortly leave another substantial inheritance. Although I've been applying for jobs I've not actually had a reply since March 2022 and, turning 50 with what is now a seven year gap on my CV, we have to face the reality that I may not work again regardless of how much I want to.
Assuming you're in the UK, the unfortunate reality is that your DH can only put £2880 a year into a pension if he has no other income. It's a nice idea, but in your family's current circumstances it's fairly insignificant in terms of long term wealth building. If your MIL is determined that a large lump sum should go into pension provision, then either it gets drip fed into your DH's pension at this rate, or it goes into yours in significantly greater quantities. You could also put £2880 a year into a SIPP for DS and any future children. Until he (DH, not DS!) is earning there are simply no other options within pensions and your DH needs to explain that to his mother.
In your circumstances it would be far more sensible to do what we've done: max out the SIPP contributions, but put the bulk of the money into ISAs and just exercise some self control if you are prepared to honour the spirit of MIL's desire that this is for the future. If you use both of your ISA allowances of £20k per year (and even DS's £9k if MIL agrees) you can get large lump sums into tax shelters much more quickly. If at some point in the future your circumstances change and DH is working, then you can withdraw from the ISAs and transfer into a SIPP, but if his earnings remain non existent then you can just view the ISA as retirement provision but without tax relief (and no tax on withdrawals) and invest the money in the same way as you would in a pension.
We were only just keeping our heads above water before my wife moved jobs a few months ago, but we made a conscious decision not to use the money to pay off the mortgage. We are getting a better return investing it than we are paying mortgage interest. I appreciate that you've been skint for a few years and it is understandable to want recognition of the sacrifices you've made but if you are covering your expenses then locking any gifts away for the long term will benefit you a lot more than reducing your mortgage slightly and then allowing the extra income this releases to simply disappear in lifestyle inflation.
As a PP said, make sure that DS's child benefit is paid to DH if it isn't already - even if you earn enough that you lose it all through the taper - so he gets the NICs towards his own state pension. And if you haven't done so already, claim married couples allowance (which you can backdate for, I think, three years).