This is a tricky subject. I have two daughters of my own, they are 4 and 2. Neither one of them is overweight but it always weighs on your mind. You want so badly for your children to be happy, healthy and have good self esteem. I agree that once someone is obese it is kind of late to do something. Don't get me wrong, it can be done, but it would be much easier to nip the problem in the bud. I'm not sure that I would have called my daughter chubby in front of her but that aside I think you have reason to want to do something. Especially if she is starting to feel embarassed about her belly. Good for you for joining YMCA, that will be so fun and good for everyone. As I was reading I had a few ideas...
Take walks with your daughter. Just you and her. Not only will it be good exercise, it will give you two one on one time. At 10, little girls need that so badly. You could even walk to a park and swing while you talked.
One on one time with your daughter and hubby is also so important. Not for the weight issue, but definately to maintain good self esteem and self worth. Daddy's need to take their daughters out and show them how they should expect a boy (in the WAAAY future!!!) to treat them.
As far as your sister, she is going to continue to do what she thinks is fine, ie. feeding her junk. I think it's great your daughter goes over there and has such a great relationship with her aunty. Maybe the next time your daughter has plans to stay with your sister you and her could go shopping for healthy snacks first. That way your sister can give her snacks but they won't be so unhealthy for her.
Also keep in mind that there are times that kids go through growth spurts. She may be putting on a little weight becasue she is getting ready to grow. Just keep an eye on her and start teaching her healthy habits. My four year old right now is eating like a horse, really (I would't say that to her, but 3 eggs, 3 pieces of bacon, 1 piece of toast, a bowl of cereal, 1 cup of juice and 1/2 an apple for breakfast is A LOT!) Now that I have noticed she is eating so much we do a lot of fruit and fresh veggies for snacks, she also loves yogurt and granola. She has to eat but I can make sure it is good for her.
One more thing. Start having your daughter help you prepare healthy meals. That way she learns early on how to prepare things that are good for her. It is so so important for them to know how to help themselves.
Your doing a good job and I really think it is okay to be concened. Just try to show your concern through love and compassion. Your little girl is coming up to the craziest years of her life. She needs you more than anythig, don't push her away by saying hurtful things. Instead of saying "you look chubby" say "hey, let's start going for walks together, I would love to have some one on one time." And of course lot's of "your beautiful." Good luck momma!