I did not move on with this setup because I don't want to live in Europe. So I also did not have this checked with a lawyer. It was mostly an idea that I had. The big question here is whether the Estonian tax authorities will say that your foreign company is managed from Estonia. If they agree that it's not, this should be fine.
Regarding the Romanian dividend tax, I would think you'd still have to pay it since it's probably officially a corporate income tax and not a withholding tax, just like the Estonian corporate income tax which is only paid on profit︀ distributions. You should check with a Romanian accountant/tax lawyer about that.
Is there any additional︁ tax on the personal level in Romania? If not, I would probably consider just sticking︂ with Romania. It's much easier to have everything in the same country.