@Bellysmackers I'd be really wary about all of this.
I've had two siblings die and both times the graves became a bit of an unhealthy focus for my DPs.
The first sister died in what sounds like circumstances similar to your DH. It was obviously really horrible but my DM in particular created a lot of drama around the grave - one example of many was that there was a storm and some flowers she'd put there blew away but she immediately flew into a rage and said they'd been stolen. She only checked and found them later after she'd upset everyone else. Stuff like this was really hard to live with, I was a teenager and I moved out as soon as I could.
Nobody got asked for their input into the funeral arrangements, and definitely not my sibling's long term partner.
With my second sibling we were all older, she'd been ill for a long time and sibling had kids and a husband. I had to explain to my DM that she couldn't jump in hire an undertaker under the circumstances. Then she agreed with my BIL that DSis would be interred in my other sibling's grave. But then that got used to create conflict as well.
My parents - without having a discussion with my sister's immediate family about the wording or anything else - went ahead and ordered a headstone, which my sister's kids were upset about. Then they complained they had to pay for the headstone, and also started muttering about it being handy for BIL that he could use "their" plot, which still had plenty of space for them. If they'd actually spoken to my sister's kids and husband about the wording and who was paying I'm sure it would have been sorted out, but they wanted to control everything.
If your former in laws have form for behaving inconsiderately then I'd be absolutely loathe to hand over ownership in case they then cause you further hurt. The fact that they've gone about this in quite an underhand and manipulative way would be ringing alarm bells, when they could have - for example - written to you and explained what it was they wanted to do with the grave and ask for a discussion on how it could happen. Losing a child must be awful but losing a husband is terrible too, and they're still not treating you in an honest and respectful way. I think you're right not to hand it over to them.