I don't think you're selfish, I actually think it's a good idea as older children often get left to their own devices when there's a younger sibling around as the younger one obviously requires more attention.
This will enable you to have a break, which we all need, and to focus on your older 2 dc, which is a lovely idea. Your youngest will not remember this in years to come and I'm sure your mum will spoil her rotten anyway and it will enable her to form a closer relationship with her, which will be of benefit to them both.
Ignore your sil, her opinion comes from a place of jealousy. Go without your youngest and enjoy yourselves; there will be many more holidays that you can all go on.
When my dc was about 2 yo we left her with her GPs and went to Disneyland in Florida without her. I only spoke to her once or twice in the 2 weeks on the phone, as we found out that that worked better (when she spoke to us she wanted to see us, but when she didn't she was fine, kinda like out of sight, out of mind) and she loved being with them.
She was fine, slept well, ate well, etc. She was obviously pleased to see us when we got back, but no more than if we'd just been gone for a few hours. She wasn't any more clingy or anything afterwards either.
She also doesn't remember it either. She's grown into a very independent and assertive teenager who's not afraid to try new things.
Maybe it worked because she already spent a lot of time with her GPs anyway, as we often stayed there as a family (as does your dc, I think you said) .