"all the kids getting their rightful inheritance from all their respective parents, not only my kids."

Some kids dont get an inheritance. Some get a huge one. None of it is "rightful"... Its not deserved. Its not based on need or on merit. Its based on who your parents are. There are few things less democratic.

"That said, I don't think there is anything wrong with providing for your kids and not others."

In the context of widening inequality, your sentence should read "at the expense of others". Im not opposed to inheritance per say but it should be highly taxed.