Trying to see if my engine is still good or if its my transmission going bad


Hello im raul my question is whether my engine or my transmission is gone im a tell you the symptons First is when i step on the gas to go it hesitates and takes a longer time to shift to 2nd so when 2nd kicks in it goes ok and the rpm goes almost to the end until let go of gas and step on it instantly and it goes into 3rd and it drags it again til i hit 70 and it goes from there ok no shaking from the engine but i just want my car back to almost normal and 2 altanators went bad in 2 weeks