does your phone take video? that is simple enough. the worst thing he could do is KNOW that you are documenting and stop drinking around the children or *gasp*, LEAVE. (that is if he is visiting them in your house).
no one would grant him full custody just because you are not employed. Your attorney will insure that it is known that you are the responsible parent.
If he is "spending like mad"...he may be doing it on purpose.