How to remove ballpoint pen from vinyl cardtable?

[american_mama]

My DD2 wrote something in ballpoint on our vinyl topped card table. Any ideas how to remove this? Regular cleaner applied immediately after did nothing nor did Magic Eraser. I've had ballpoint on several surfaces in this house and find it incredibly hard to remove - specifically, painted wood and stained wood.

While we're at, DS drew in ballpoint pen on the fabric cover of an exercise mat/sleeping mat. No luck with traditional fabric stain removers. Any ideas?

Ballpoint pens are pretty hard to remove from the house, but clearly, my children (who are definitely old enough to know better) have problems using them appropriately.

[swissair81]

Rubbing alcohol usually works well on pen. I especially like the single use alcohol swabs for this purpose.

[lizzywednesday]

If rubbing alcohol doesn't do it, try hairspray.