Yes, that's certainly the case. In some mandatory minimums, depending on how they're prosecuted and regardless of the person's actual involvement, if they are factually guilty, they will get the mandatory minimum. If the mandatory minimum is a year or two or three, that's what they're going to get.
The other thing that gets in the way is that any mandatory minimum sentence prevents a conditional sentence from being put in. Generally, if you get a weekend sentence you can't get one longer than 90 days. If the court felt that 90 days wasn't enough and they felt that four, five, or six months...you can do a conditional sentence, which is served in the community, with house arrests and other difficult sanctions, but that's not available if conditional sentences don't permit it.
What happens then is that the person goes to jail, and if they don't have someone to look after their kids, you're exactly right, they will lose their kids.