If your nephew (son of SIL ?) is calling you names, then presumably he's heard those names from his mother ? ...... or at least heard that you've upset her.
You know what, it strikes me almost as if MIL & SIL are jealous of your natural position as "chief mourner" (for want of a better expression). Hence them destroying - 'cos that's what it was - not just digging up, something which a little girl had carefully and lovingly doen for her dad.
This is all so sad ..... that people are "vying" for position in an imagined hierachy of mourning. Put more bluntly, it almost comes across to me as if they are saying we are more important than you, we were his blood family. Completely ignoring the fact of course that those little girls are blood family too.
It's never nice to lose anyone you're close to and I know that a lot of young deaths do hit parents hard because there's this assumption that you'll probably die before your child but, fact is, on a day to day basis, before his death, your husband was most involved in your life, that of his chosen wife, and the daughters he willingly chose to have with you. Practically (and I don't mean to ignore the emotional side by saying this) your husband probably played very little part in the day to day lives of his mother and sister.
So, of course they're grieving .... but their lives are not going to be daily affected by his death in any way near approaching the impact it's had on yours and your daughters. Given that, and even though they're grieving, I think their behaviour was monstrously insensitive, rude, arrogant (you name it). Grief should NOT excuse you being horrid to other people .... especially those hardest hit.
Yes - it's a family place, but it's horribly arrogant, IMO, to make permanent (well, semi-permanent, 'cos plants can always be dug up as you have found out to your cost) alterations to a grave without first discussing it with the widow - that's just basic manners to me. Tending the grave is different - placing flowers or cutting grass.
If I was you, and assuming I hadn't already lost my temper with them, I would write a short, polite but curt, note asking them to leave all planting on the grave alone unless they have sought your permission beforehand. If they then get even more arsey I'd remind them of your legal entitlement in the matter ..... but why oh why you should have to be dealing with such insensitivity at all is beyond me. If you are already a considerate person, you don't become inconsiderate through grief.