I don't make excuses, I just always suggest all-together types of activities and pass on the others, say 'I don't think that works for us' or 'we can't do that' (leaving out that it's 'because I don't want to').
If you look at past threads (probably in general parenting, or life as a babe/childhood years) you'll see that this isn't unique - a lot of others struggle with grandparents who seem to insist on having alone-time with their grandkids instead of spending time with the whole family too. And, likewise, there are a lot of grandkids out there who don't really do alone-with-grandparents sleepovers/weekends/etc. at young ages like your dd (or ever, sometimes). It really isn't even the best idea for some kids, regardless of how parents feel about the relatives. Heck, I didn't do anything of the sort until around 12 or 13, and probably only 1-2x at that (I did have long distance grandparents and extended family members, so that limited it too I'm sure).
Some gentle things you could point out - did you (as a child) have the same kind of time alone with your gp? And at these ages?? If not, remind your mom of that sometimes when she presses the issue. She may have felt similarly and have forgotten what it's like having a young kid.
All-together family time is nice because young kids don't always remember special things they do with their grandparents - and then they'll be more likely to have stories about it from their parents, or pictures their parents took of that time. And that's a nice thing.
Being really regular about sending/emailing photos/videos can also really help satisfy their 'I must always know what my grandchild is doing' without always having to be with her/you. Maybe step that up a bit for them, and it will help their always needing to see you too.
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