The good news is that this probably isn’t an actual gearbox problem, but rather one with the mechanical linkages that select each gear or perhaps even the gear selector itself. If you can remove the centre console, you might be able to locate the offending (loose) fastener that is allowing the gear lever to flop about and not find its proper place.

If, however, you mean that the vehicle doesn’t want to select Drive properly first thing in the morning and either won’t move or moves very slowly when you accelerate, then you could well be looking at a worn transmission. That said, the same problem can be caused by a transmission that is simply low on fluid, and a top up will put things right. So that’s the first step: Check the owner’s manual for the correct fluid-checking process and try that. If a top-up doesn’t fix it, it’s off to a mechanic. But beware – driving the car in that state could be doing extra damage to the transmission.

The VE sounds like a good car that's been well looked after and would be a good car for a growing family such as yours. I will assume it's a V6, in which case the main thing to be concerned about is wear to the camshaft timing chains. They're a known problem and cost $2000 or so to replace if they do wear. You can tell if they're worn as the engine runs poorly because the cam timing is thrown out. Other than that the VE is quite sound.

It's always hard when you know there's a problem, but it's never present when there's a mechanic with you. It's hard to diagnose when you can't hear it for yourself, so keep notes on when it occurs and anything you observe that might give the mechanic a clue. Things like, does it do it on cold starts, under acceleration, slowing down, at idle. Even better, record it on your smart phone so you replay it for the mechanic the next time you take it in.