Repeat after me. The major airlines don't care what you flew before. Much more important will be the networking you do.

As far as having young children at home goes, here is my take. I have done just about every type of airline flying there is. Regional, major passenger, supplemental pax and freight and a stint as an expat. Next to day trips out of a base you live in, the three to four day trip is much easier when your kids are younger. You leave and come back and not much has changed. If you are doing long blocks of days (15-20) days you come home and can actually see a noticeable change in your kids. If you get a back to back it could be over a month of not seeing your children. Young children are also a lot more work for your wife and the long stretches away can be hard on her.

After kids get older(15 and up) I have found that the long blocks of time home seem to make up for the long stint away. Of course your situation might be different. When we become pilots we probably don't realize until we have children how much we will have to give up to our careers. You will never get back this time while your children are young. If SAI is a good fit for you and your family go for it. Don't do it for the big shiny jet. Boeing and Airbus will build more. You only get one shot with your kids.