Like some others have mentioned, I should say that for us, my husband's crossdressing is a very sexual thing. It's like a fetish, and I feel that he should only share that aspect of himself with me (and me alone). That said, I embrace my husband's crossdressing. Being a bisexual woman, there's something very exciting about seeing my muscular, hairy, macho husband dressed in pink lace or red silk. And he likes my panties just as much when I wear them as when he does.
Because of the nature of my husband's crossdressing, and because he identifies it with eroticism rather than comfort or relaxation, we have aggreed that we will keep it between us in our own bedroom. My husband has expressed some interest in going out fully dressed on a date as lesbians rather than husband and wife (which EXCITES me BIG TIME), but again.... We plan to use the whole "date" as foreplay and reap the benefits when we get home
For us, I would be embarrassed by my husband going out in public dressed, but not because his crossdressing embarrassed me. It would be because he was bringing something intimate and private from our bedroom out into the open. It would be like him masterbating in public or something. I'd be mortified. But that's just our specific situation. Hope my experience helps shed some light on your situation. It may just be something that your wife wants to keep between the two of you as an intimate secret, and what she says about your kids is right. Kids are CRUEL, and explaining crossdressing to them is certainly tricky. You wouldn't want them going to school and hearing "My mom saw your dad dressed like a woman in the grocery store". Even if your kids know and understand, most other kids they socialize with don't, and they would ruthlessly attack your kids because their dad is "different". It's just the way things work. So if it's NOT something private or sexual for you, you still have to acknowledge that it's probably not something the rest of your family is willing to broadcast from the rooftops.
I don't know what to tell you except that patience is a virtue. The TG issues certainly complicate things quite a bit, but I believe you can make it through. Good luck.
-Tiffany