I hear you - I know how demanding (my brother's) kids can be - much worse than my puppy and she has just worked out that if she barks a lot - I get up, put her on lead, and take her outside to see what the barking is about - great fun for her, but I'm not getting anything useful done.
Have you tried training "quickies"? Ie instead of trying to get half an hour at once, try 2 to five minutes at once - when I started training at home - that's all I could do because that's how long Frosty's attention span was. So I'd do lots of little five minute or 30 second quickies.
We still do them at the park and I'm actively looking for places with distractions now - so your kids could help (maybe - depending on how old they are). I get Frosty to do a heel, sit, stay, and go, and she runs around like a nutter, and then we do it again - she comes of her own accord and stays for the treats or attention or both and then leaves of her own accord and I tell her "go" and let her go. I don't even do any of this on lead. Same deal in the back yard. Sometimes I'll clip a lead on - but I still let her go as soon as she loses interest.
I did read somewhere that the click and treat thing can be used to (slowly) train pound dogs to bark less ie as a trainer or staff member walked past a cage - if the barking dog stopped for any reason, instant click followed by a treat tossed in the cage - and that's all. Takes 2 seconds to do.
So maybe just before you let Candy off lead at the park you make her do a quick circle on lead and not pulling or at least being held in the heel position and then sit for unclip and go. Start with trying to get "watch", build up to heel. Lots of squeaky attention getting talking or just a really short lead - and not to get unclipped until she looks at you (watch) good dog - unclip - go and then build up to what you want - but don't do the lesson of the day for any longer than 30 seconds.
If Frosty is at the oval and I don't unclip her - she pretty soon looks at me to try to figure out why or tell me off - there's your "watch". And she's also worked out she doesn't get unclipped until she stops pulling and sits - mostly cos I can't get the clip undone unless she does.
Does that make any sense?