Dust cap pushed in by kiddos... best home remedy?

Vacuum cleaners might be too vigorous and detach the voice coil. I suggest using an appropriately sized cardboard insert from paper towel, etc. and your mouth. Gently suck in until corrected.

I've successfully used a vacuum cleaner numerous times over the years. Just be very careful, brace your arm/hand against the speakers front baffle, and use the other hand to help steady and hold back the nozzle of the vacuum cleaner. Do not get so close that the vacuum nozzle sucks itself down to the dustcover. If you take it slow and easy, and don't try to get too close, it should work fine. But, I guess it could also be disastrous if you got to close or if the dustcap was not firmly attached. 

I find that painters tape tends to work very very well.
to rub the tape on to the bent up area, gently, and then pull off at an angle, which will cause the dome or dustcap to lift out, bit by bit... at the same time..and as the tape slowly pulls away and off. Both happen at the same time.

Move slowly. this method offers maximum control and action, action which can be terminated simply by stopping pulling. Changing tension, changing directions, and so on.

vacuums are rather uncontrollable and abrupt.

I have used a few ways to do this.
A good tape applied works well. Apply tape then scratch it down with your finger nail. Slightly hold down on the tape so that it won’t pull up, then pull at an angle, do not pull up and simply rip the tape off.

I have used a sticky putty. press lightly, the cone sticks and pulls right up.

The vaccum has not worked well for me.
In extreme circumstances, I have had to lift the dustcap and re glue it... Apply acetone around the glue of the cap, take a straight edge blade and slowly cut away allowing the acetone to eat the glue. Once It is up, clean up the glue area, straighten your cap and re glue it down.

I would pop it out with two pins.