Connecting a medium sized 1 kVA Inverter with a 2 kVA Generator
What you are describing is a microgrid. It is not a circuit, but a system of coordinated pieces of power conversion and control equipment. A variety of microgrids have been proposed, designed, implemented and described in published literature. Societies within the Institute of Electrical and Electronic Engineers (IEEE) regularly publish technical papers about microgrids. In the USA, the U.S. Department of Energy, National Laboratories and research organizations have information about micro grids on their web sites.

This is a whole field of study, not a simple question and answer issue.

Some of the U.S. Government sites have beginning level material on their sites. There is likely do-it-yourself type information on DIY and home energy project sites. Some vendors my have "plug and play" products and offer guidance for micro grids. There is likely a way to do what you want with the performance that you want, but it is going to require some searching and study.