I only posted here as I've seen other Adobe posts...it is what it is.
Your question contains your answer.
First, you’re not actually joining the objects, you’re just grouping them. To join the you would use the pathfinder tool (unite) which would essentially make your 3rd picture (far right) into a trapezoid like shape with a rounded middle on the left side.
Secondly, if you are skewing the parent, then the child is not going to skew, as you’ve only selected one object of a group. However, if you have the entire group selected and choose to skew, then all of the objects contained in the group will follow.
This is why it doesn’t work in any vector program you’ve used. Make sense?
P.S. I’m thinking the mods will move this to the graphic design sub thread in due time.
[doublepost=1521155062][/doublepost]By the way here is a pic of it done the way I said. . . This is with Illustrator CC 2018.