In the Doghouse
This avowed dog lover says it’s not about dogs.
People do not get to dump their responsibilities on you, or to complain when you refuse to serve as the cheerful dump-ee. There’s nothing wrong with your boundaries, at least with your sister (I’ll get to the fiance issue in a second); you just need to accept that people won’t always respect them, receive them warmly or allow you to set them without consequences. That’s just part of the deal with boundaries, and the boundary-crossing people who inspire them.
But your work isn’t done here yet, especially if your sister is repeating a family pattern of saying one thing and silently (resentfully) expecting another. Does your fiance also use guilt tactics to enforce the primacy of his needs? It’s possible you’re poised to carry an unhealthy family pattern over to a marriage.
Keep that in the back of your mind as you address that DOA compromise with your fiance. Marriage is a different beast from a home shared with a sibling. You and your sib carry out separate lives with separate goals under your shared roof. You and your fiance presumably share goals, plus an avowed duty to serve as the stewards of each other’s happiness. Just as he needs to come home to walk his own dog ungrudgingly, every day, as a gesture of love for you and respect for your needs, you need to have room in your plan to notice when he needs you to have his back, or take his dog out for a spin. Ungrudgingly, just out of love for him and knowledge of what he needs.
That, and your no-dog-care stance is only fair in theory. In practice: highly unrealistic.
So you both need to come up with a fuller, more realistic compromise — one that centers not on care for the pet-to-be, but on caring for each other’s needs, and on acceptance that your needs differ but matter the same. This kind of agreement promises better care for the dog, too, because poor Mr. Pickles inevitably gets the brunt of caregiver resentment.
If you find through this conversation that your fiance is fixed on getting you to prioritize his needs, with suppressed resentment and/or without fair regard for what he has a right to ask of you, or vice versa, then please at least consider that you’ve re-created your family’s emotional comfort zone in this marriage-to-be — and not in a good way. Good pre-marital counseling makes sense regardless; tell them Mr. Pickles sent you.