Well, didn't you draw the long straw. You happened to marry someone decent and had children; your sister ended up with a 'horrible' husband. She's probably had years of abuse within her marriage, and that might be a huge part of why she 'chose' not to have children.
Bully for you for life working out the way it did. Your sister was not so lucky.
I'm single and childless, no other family. However, I've been able to use my time to cultivate friendships so that I'm never without something to do at Christmas. Your sister has dedicated her life to your mum; her friendships will have suffered, and, in fact, you say her last romantic relationship ended because of the care she gave your mother, so YOU DIDN'T HAVE TO.
I've also been the sole full-time carer for a terminal parent with a malfunctioning brain. It's 24/7. Never a full nights' sleep. Emotionally and physically draining. You seem to have no comprehension of what she had to endure, comparing it to a few drives and admin. Get a grip.
By the sound of it, by luck of the draw, your sister has had a pretty shit and stressful life - probably far from the one she'd imagined, and now you want to exclude her from her only remaining family for utterly selfish reasons.
I don't think you should invite her. I'll bet if she came, you'd make her feel unwelcome. Quite honestly, that would be worse than allowing her to find an alternative arrangement where she can spend it with people who actually care about her.
She's better off knowing where she stands, and moving on with her life without you in it.
And maybe one day, when your husband is dead, and your children are following in the footsteps of their mother and focusing on their immediate families at Christmas, and your sister has found a healthy relationship, possibly surrounded by lovely step children and step grandchildren - better things to do than spend Christmas with you, you'll regret your rejection of her.