I am not completely up to date with your sitch. I also struggle with the lying!! It is so hard to deal with. My H is also always late too.
When I try really hard and think positively I say: I will not own what H is doing. If/when he is lying he has to deal with those consequences eventually and I will not let myself get down. H does not deserve to have that kind of negative effect on me!!!!
God is watching H, so I do not have to. The snooping is the killer. Just pray alot and vent here. That is what helps me. My goal is to be in the best physical shape I can be. Mentally and emotionally I continue to be the best I can. Focus on the kids and stay busy!!