On balance, and respectful of all the other posts here, I strongly recommend the section from Sarria to Santiago as a first-time route with kids of the age you indicated. It has more of everything you will need to get there sane. There are enough distractions for the kids. Enough beautiful scenery, people, and old villages to satisfy all.
You did not indicate whether you planned to stay in hostals (inexpensive B&Bs or family run inns) or the pilgrim albergues. In April, you will likely have no problem finding space at albergues, but they typically are not heated, or not very well.
Also, expect daily rain, especially in April. We have a saying..."The rain in Spain falls mainly...on Galicia!" Your entire walk will be in Galicia. Point made, bring ponchos for all.
So, in combination, being wet and cold makes a strong case for a relatively warmer private lodging. Plus, having your own bathroom and a locked door is a luxury on Camino.
If it were me with my nieces and nephews (no kids of my own) I would try to book hostals in advance using booking.com for each night. If you are following the
Brierley guide book stages, every stop has multiple choices. You can book singles, doubles or even triples (in some places). I use a smart phone. Free Wi-Fi is common in most cafes along the way, so you can research and book ahead. However, I recommend booking Sarria first.
If you want specific suggestions, send me a PM, start a private conversation and I will be happy to share my personal preferences from having covered this route twice recently, 2013 and 2014. Or,m you can simply search here for recommended lodgings at each of the standard
Brierley stages.
Also, as regards starting at Sarria, know that this is where 50 percent of all pilgrims start their Camino. I work in the Pilgrim Office as a volunteer and see the stats. On Friday and Saturday nights in the large town / small city (Sarria) hotels fill up fast. So book early.
This is because the largest tranche of starting pilgrims are Spaniards who take a train or bus to arrive on Friday or Saturday, so they can start walking the next day (Saturday or Sunday). This allows them to better manage their holiday / vacation time. To avoid this "wave," simply slide your arrival at Sarria, and beginning your Camino a day earlier or later. This also has an affect on the trail, as this "wave" of people start out form Sarria and can be distracting. Starting out a day earlier (Friday morning) is better than starting out a day later (Monday)
I hope this helps.