You would have experienced by now that your kid is found to be more attached to either you or your spouse the most. This might be based on who in their minds is more powerful or caring or trustworthy depending on your kids’ viewpoint.
What you need to know
Though this is not going to pose any problem always, it will definitely have an impact on their personality development. If your kid is overly dependent on one of the parents which is causing problems in taking care, then this is the right time for them to be made to come out of it.
Clinging to one of the parents always is not good for your kid or you. Try to see the underlining reason for that and solve it. It could be they need your attention and are insecure in certain things for which they cling to you/your spouse though they seem normal in all other activities.
What you can do
If the kids are clingy, try to break the habit slowly, day-by-day. Set some limits and engage them and slowly tell them that you will do an errand and join them a few minutes later. Increase the time that you are away slowly. Some kids gets frustrated when they do not get complete attention and can throw tantrums, be angry, cry. Let them cry and get angry but do not lose your temper and react. Tell them it is ok to cry and let out the emotions for some time.