I'm sorry it's so hard.
Kids can be pretty resilient, but only you know how much they can take. :-( I'm sure your kids would love to have you home all day, but that's not an option right now. Even if they don't understand that now, they will. Try not to let your feelings of guilt cause you to make a decision that's not the best for all of you.
Is the stress mainly due to worrying about the kids and the commute? If you think you can fit into the job better if the at-home and commute stress drops, then see if you can find a closer place to live. Universities often subsidize local housing for employees. If the stress is also due to really hating the job (even with the good aspects), then your decision is made.
Try to investigate all the options before making any decisions. See if your boss or coworkers have any suggestions for easing the situation if that'll help.
Don't feel bad if the close job is a better fit. You'll not be chained to it for the rest of your life if you take it. :-)
Hang in there and let us know if we can help in any way.
Best wishes!
Scott.