Congratulations on baby #4!! That is wonderful!
If you are “too busy” for time with God, then you are too busy. Something has to go. Catholics believe that family life is a vocation…a calling. So, first comes God, and then glorifying God through one’s vocation (in this case, as a husband/wife/parent).
The extra-curricular activities are there to foster growth within the vocation. We help ourselves to be better parents by teaching our children responsibilities and skills, for example, which sports and other activities can develop. But when these activities take time away from God and our family, resulting in the family spending less time with God than they should, and less time with each other than they should, then these activities have become an obstacle to healthy spiritual and familial growth. In that sense, yes, they can be occassions for sin if we choose to put a priority on the activity as opposed to putting priority on God and family. Each person will have to decide, with his/her family and through prayer, how much family and God “time” is enough, and whether the activities are a distraction to that.