The most challenging part of the livestream service is what to do during the sermon. We want our kids to engage with God's Word but we need to hear it for ourselves also. For us, we send our daughter to "Little Sunday School" with activities she can do by herself and morning tea to eat. As a back-up we have our iPad with headphones ready so she can watch a kids' talk whilst we listen to the sermon. For older kids, this could be a great opportunity to teach them how to listen to sermons. You could print off the sermon outline or transcript or give them a special notebook for their own notes or drawings as they listen. You could even think of one or two questions to ask them at the end.
I recognise that a lot of this is made easier for us having only one child, so if it is not possible to hear the sermon during this time either alternate which parent is 'on duty' or plan another time when children are sleeping to sit down and watch the sermon together. Whatever you decide, make it a priority to be able to hear from God's Word for yourself. Remember, God's Word is powerful so there is much for your children to learn even by hearing his word preached in the background whilst building a Lego tower.