best bet would be getting memberships for yourself and the kids mate,you get the chance to apply for tickets for games in a twice yearly pre sale, games up to around xmas, then games for the 2nd half of season, beware though it is a bit of a bun fight as demand usually exceeds supply and certain criteria apply for the bigger games,ie games attended previous season,but for some of the less glamorous games it may be possible to pick up tickets in the pre sale, i usually only attend about 4 a season and tend to get games for the smaller teams in the pre sales,and any bigger games i want to go to i either see if friends i have down there can sort me or i take my chance and go up to the ticket window on the morning of the game and see if i can pick up any returns,i did this for the last 2 everton games at anfield and man utd 2 seasons ago,its a risky process and probably wont pay off for you if you are looking for more than a single ticket,may be you could look at any league cup games midweek at anfield against a smaller club as a way of getting the kids over as tickets will generally have better availability then