Implementation may be politically difficult, but the solution isn't rocket science: substantially raise the inheritance tax and abolish all trust loopholes.
100% tax on inheritance and other hereditary wealth-transfer schemes, eliminate loopholes, use the (substantial, I assume) takings to supplement existing funds and implement a universal basic income. Also do something about education and healthcare. You can work and compete as hard as you like during your life, and get as rich as you possibly can in that time, but you can't take it with you and your wealth is used to…
The way inheritance should be solved is by not allowing a single person to inherit more than 50% of the total net worth.