As far as the remarriage issue, I'd think the age of the children may be wise to consider. Having very young children that are against the remarriage could potentially have a longer negative effect on the marriage. This will likely cause the parent to be viewed by both sides as favoring the other, or they will flat out favor one over the other.
Favoring the child will strain the marriage as no one wants to be tied to a relationship where they feel they're the least important.
Favoring the new spouse leads to anger, hurt and likely rebellion in younger kids that only grows worse as they get older.
Whereas with older kids, teens for example, they're likely working to be more independent anyways, and will have less of an impact on the family dynamic. And even if there are problems it's less time for strain the marriage.
Also why the child is against a remarriage matters. Some believe that their parents will reunite and views anyone who may get in the way of that as the bad guy.
Sometimes kids simply do not like the potential spouse as a person.
I dated a woman with a teenage son. He was not happy about this as he hoped his parents would reunite.
We continued dating and over time he began to be more accepting of the relationship. He realized his parents weren't getting back together (and also how poorly his father treated his mother) but that his mom seemed happy to be dating me.
Eventually he accepted the relationship, and me, because he saw how happy his mom was.
But I think that the spouses need to be solid in their relationship and on equal ground within the family dynamic.
If not then someone gets favored and nothing will be good.
Before marriage discussions and clear understandings of what role the step parent will play, particularly in discipline, need to be worked out and resolved.
As with so many of these sorts of questions there is no one size fits all answer.