Problems with my Car?

Hello,

I have a suv izusu rodeo 2002 ls and i bought it with my parents in the year 2010. My dad died and i was left with the car he was driven. The Suv after that was still working perfectly only problems with the batteries and simple things. Today its a different story. I was driving form work to home and of all of sudden my car was starting to act kind of strange. When i was driving to put the gas pedal it was making a tremble sound like minor bouncy and continue to drive. It has happen to me twice today. When i was making a left turn for some reason my car did not wanted to move. I though about this it can be a problem with the transmission. I do not know what to do if i should invest buying a new transmission or start looking for other options. Your help is appreciated with advices i do need them because its something i need to use to go to work and other things.