R.,
It all boils down to what you are willing to put up !? Have a clear and frank discussion with him about why he wanted to reconcile (I would not mention your suspicions, you'll put on the defensive) , was it you he wanted back? the kids? the whole package ? Explain you really prefer to learn from the first time and don't want to put the children or yourselves through all that again. Try to get him to open up without causing drama, and his answers may give you some insight. You should know him well enough to know if he is sincere and his actions with you and the kids should reinforce what he tells you. If you don't buy it , it really just depends on what your priorities are, finish school, let the kids get a little older before they have to deal with another separation/divorce, what are you willing to sacrifice ,if anything and so on, and if things don't work out ,you've taught your kids to try and work things out ,but, things don't always work the way we want or they way they should, and if they are old they'll also learn - relationships take two people working at it (they don't just happen and everyone lives happily ever after,...). Make up your mind what you want,too!
Explore the feelings you have, for him, good bad, or indifferent , there is no expire date, take your time, this is an investment in your life as well as the lives of your children, and not something to take lightly or quickly.
I wouldn't think ,if it comes to it, that you'd owe him spousal support if you have custody of the kids, but, it varies ,and often depends on how long you've been married and what state you live and file in,....
I wish you and your family the best ,(and you may want to talk things over with a pastor or counselor before you make a final decision) C. S.