In a reasonable size department, there will be CSI people assigned to all shifts, just like police officers. It might take a while to get to the shift you want, or, instead of permanent assignments, there could be rotating shifts. Before accepting a job, it is important to know how they handle shift assignments .
In smaller departments, you would have a likelihood of getting called in. Also, in larger departments, if you are specialized in something that is pertinent to a particular crime, you would possibly be called in. And of course, if there was a major crime spree with lots of evidence to collect, regardless where you work, expect to get called in.
Many people successfully raise families while working shiftwork subject to call back, both in the law enforcement and medical communities. If this is something you really want, you will manage to find a way to make it all work. When I was an officer, we frequently traded shifts with other officers so we could go to functions with our families. There was rarely any trouble finding someone to trade with, as people knew that if they needed something someday, you could be counted on to repay the favor.
Besides, your kids would be really proud of having a mom who is a CSI! One day my son and his friends were doing chalk silhouettes on the driveway!