My DH works long hours and never sees the DC in the week as he is out before they wake and back after they've gone to bed. He is usually away at least 1 night a week too, and his daily commute is 3 hours in total. We are all used to it, and the weekly routine is set up dependent on me (my work, nursery, school, clubs, etc). I have my support network of friends and neighbours who can do emergency pickups and drop offs if I need them to, as well as babysitting.
For a short time, he worked closer to home and would sometimes get home in time for stories but it depended on the trains and his workload. That was more unsettling for the DC than it is now, as they would wonder whether they would see him that day or not.
There is a chance that he will get promoted soon, to a position further away. We have already discussed it and agreed that, if that happens, he would move and we'd stay put. He would still have to work long hours, but he could reduce his commute. I have a job that I love, with flexible hours and an understanding manager, a great support network and the children are happy. We have quality family time at weekends, and he never works then (partly why he works longer in the week).
He knows that he would still be unlikely to see the DC in the week if we moved closer to his new job, and that I might not be able to find a job. I struggle to make new friends and am so happy where we are. He wants us to be happy, and we both know that he enjoys his job and would be unhappy if he turned down a promotion that he would have worked so hard for.
We've moved in the past for his job (before DC) where I ended up in a job I hated, struggling to make friends as job was nowhere near new home. He felt so guilty for making us move (even though it was a joint decision). I know it is different now we have DC but we know that this is what we would do if and when the promotion comes up.
I know it is slightly different as we are already used to him being away 1-2 nights a week but we would both jump at the chance of the working pattern that you are describing, the opportunity to have more than 2 days off in a row and to see more of the DC.
Good luck with your decision and hope it works out for you.