I think your objection -- and it is an understandable one given that we all live in the physical world -- stems from your distinguishing entities by analogy to physical entities. That won't work well here. As long as you think of Father, Son and Holy Spirit as akin to three physically distinct, individual entities having mass, dimension, etc., it will be almost impossible to conceptualize Trinitarianism properly, and tritheism will be the result of considering Father, Son and Holy Spirit each as God -- as ONE God.
Trinitarians haven't done you any favors in trying to get you to move away from that kind of thinking. The rubric "three persons in one God" is actually a horrible way to put it, because "persons" immediately connotes physical human beings -- and suddenly it's like Moe, Larry and Curly in your mind's eye! The homoousion formulation adopted at Nicaea works better. But that will take some time to explain. For now, our common starting point will have to remain what the opening phrase of the Nicene Creed affirms: "We believe in ONE God, THE FATHER Almighty . . ." Yup, surprise, surprise, Trinitarians say there is ONE God, and they identify Who it is -- same as you do!
What follows in the Creed is a detour into Greek philosophy that I will do my best to explain if you want me to.