Super clingy in public

kj002f

My 15 month old (12.5 months corrected) twins have become super clingy whenever we're out of the house.  They are great at entertaining themselves, often for long periods of time, at home but once we leave it's another story.  Now whenever we go to a playgroup, out for coffee, to a friend's house, whatever they both want to be held the entire time and won't play with their toys or anything else for more than 5 minutes.  We're also having separation anxiety issues but in these situations I'm sitting right there with them.  I don't know what to do anymore.  Anyone else go through this?