Big hugs. I agree with what everyone else has said... small steps designed to face your fears are the best way to beat anxiety, and it sounds as though you've had a lot on your plate lately so go really easy on yourself. Anxiety usually kicks in when we feel our ability to handle something just won't match the threat we're facing (or at least, the threat we perceive). With your parents' recent separation, it's really normal to feel your resilience is sapped and that you just can't handle what you used to.

Can you have a think about what you feel scared of at the prospect of going out? What's the worst case scenario you're imagining? Sometimes just shedding a light on that and thinking logically about it is enough. If not, make a plan around how you would handle it in the (usually unlikely) event that your worst fears came true. Your munchkins sound fantastic... 15 mins of sitting still in a public place at those ages is great! (I would worry if they didn't have ants in their pants after that amount of time!!!) It's natural for your protective instincts to kick up a few gears when in public where you can't control all aspects of the environment (or watch their every move), and I think it's hard how as mothers we're constantly forced to second guess our instincts or ignore them for the sake of following what's considered 'socially appropriate'. Having said that, I think the feeling of anxiety can make us 'see' things that aren't there, like you mentioned about thinking your kids were getting sick. Definitely take it slowly but be wary of avoiding too much... I've found that gives short term relief but doesn't really help in the long run.