Apologies in advance for this answer being so long!
Life is hard. And it's rarely fair. It's that kind of planet. We are never loved as much as we think we should be, and the people we would like to be the closest to often don't respond to our love for them.
I hope that some day your family will draw close enough to you for you to be able to talk this over. It may happen and it may not. In the meantime, you might want to get some counseling for yourself one day, just to set your own feelings straight. Your initial statement, that you have never felt as if you fit in with your family, is a little disturbing. Whether your relatives ever change or not, you want to make peace with your feelings so that they don't accidentally spill over toward your own children.
Here's an additional thought: look at where you are now. Since you haven't said otherwise, I'm assuming you're married to a man who loves you and whom you love. You may have to live with "tight belts," but so do most people. You have children and I'm sure they love you and you love them. You have a pretty good life right where you are. It's too bad if your relatives don't appreciate you as much as they might, but that obviously doesn't mean you're not worth anything.
If I were you, I'd keep inviting my parents to be with me, but would not be hurt if they turned the invitations down. I'd just keep inviting and giving them a chance to say yes.
Meanwhile, take action. How can your strengthen yourself? You don't need your relatives' approval of you to live a good life. Focus on what you do have, and look for something GOOD in your husband and children (and yourself, too) every day without fail, so that your unhappy feelings can't take over and steal your joy in the people you love!
Actively look for things around you to smile at, even to laugh at. Make your home a happy, fun place for friends and neighbors to come to. Be involved in your children's schools, in your church, in your town. You might even meet an older couple who live too far away from their own grandchildren, and quietly (!) invite them to be substitute grandparents, so your children will not lose out on intergenerational affection.
You may never be as wealthy as your sister, but love and character are also kinds of wealth, so never believe you're poor.
What you'll end up with is a happy life with a good marriage and happy children, friends, and many ways to contribute to others around you. And it's so sad that your relatives may miss out on being part of that!
And if you REALLY want to think about it this way, you COULD call it, "Living Well is the Best Revenge."