Hello guys I need help , my vogue 2004 stops accelerating if I throttle harder , but if I slowly accelerates , it will select properly , the reverse mode works perfectly . Another is the transfer case heats up during issues

Hi,
Vogue is just a trim level. What engine?
How many miles on it? G-Box might be shagged but if you are accelerating hard it may decide to stay in the lower gear for longer because you are demanding rapid acceleration and not a smooth and steady increase in speed. Have you had it on any diagnostics? Is it throwing any gearbox fault codes up?