can car tires explode while driving with little air pressure in them

Get it fix before you take off-you don't want a mishap enroute-

can tires explode while driving with low pressure though?

It depends how low and condition of the tire- the air pressure in the tire increases in temperature it might not blow but wear out so fast that you'll be riding down the road with only the rims on-never know what will happen-I'm not a mind reader-get it blown up to specs

theres no doubt that i need new tires, they are old but its like 30 degrees all day today..... and i think if i pump them up before i leave and before i come home, i should be good. what do you think?

Pump them up, but get new tyres asap, tyres will not explode but will tend to roll off the rim if pressures are low and corners are taken to sharp.