I have a grand vitara 2008 but the transmission to drive does not kick in when I slow down or take a turn so I have to use a higher gear but the reverse is okay please whats happening

Correct. When you turn off the engine you lose the engine vacuum to the brake boost assist. No brakes. Can't accelerate with engine off.

the car has part time 4wd.
you failed to say, what surfaces you are diving on.
dry pavement (or wet) illegal
grass,sand,snow,ice, dirt, mud,gravel. (PERFECT)
or?
why are you driving in 4H in the summer, are you OFFROAD?
or in alaska,?
state location (state or country) and what is under tires.
this car is not AWD, wiki, AWD, AND PART-TIME 4wd
the part time has no center differential. that is a very important fact to understand,

low fliud pressure in transmission..check levels and change fluid/filter and retry vehicle.

use a scan tool to reset the ECm

have a tranny filter fuid change soon

Have you tried checking the catalytic? This is for filtering the gases from the combustion and can be one of causes of the power failure.

It is the Power -vs- Normal switch. In Power (P) mode, the shift points on your transmission are extended so you can accelerate quicker. The Normal (N) mode is for typical driving and will increase your gas mileage.

When the car is just cruising along at approx.50+ MPH push the O/D button. You should feel the gears change higher and if you have an RPM guage then it should drop as well to fewer RPMs. This would be normal driving conditions. O/D will not kick in until the last regular gear (3rd or 4th depending on model)  had been shifted into. O/D automatically kicks out when slowing down and the transmission shifts to a lower gear. Thus the O/D has no function at slower speeds/gears and does not need to be shifted ( on or off ) except in the very first example given here.

Check the condition of the tranny fluid.
It should be pink.

there should be a switch next to your automatic transmission shifter that says N, A/T, P....switch it to N and the POWER light should turn off. When the power light is on that means your car is shifting gears at a higher RPM.