If you have a good husband, who is supportive, thoughtful, and loving toward you all of the time, then there would be reason to suspect he has valid concerns about why you shouldn't do this. I know my husband is an awesome partner in life and although my heart would want to do that for my sister, there are some real life issues that would make it a bad decision for me. I would NEED him to talk me out of it, and he would, but I would still have a little heartache, but heartache and good decisions sometimes go hand in hand.
Now, if your husband is just a giant donkey about everything you do, good or bad, then that's a different situation. Maybe he's just being a jerk for the sake of being a jerk, and there really isn't any valid reason for you not to make the offer to your sister.
It just depends on the dynamic between you and your sister. If you can "butt out" while she raises HER child, and do this graciously, and without drama, then go for it. Divorce is real, so be prepared for that and any other differences in the way she raises HER child and the way you raise yours. Your egg is not a license to preach, control, or give guilt trips. Also, if you are prone to depression, excessive dramatic emotional scenes, guilt trips, self pity, whininess, etc maybe that's what your husband is concerned about. Maybe he just doesn't want to put fuel on the fire, so to speak? If you want to walk around and gloat with an "I gave an egg" badge on your shoulder, maybe he doesn't want to be sick to his stomache every day. If you do none of the above, then it goes back to your husband. Great partner or Donkey?