There is no doubt from what you wrote that you have neglected him and the marriage and this is what happens. However, the flirting and possible cheating is 100% on your WH, he chose to do that rather than come to you and discuss your marriage. He also chose to lie to you by hiding what he was doing, till you found out. Therefore it is not up to you to mend this marriage, he crapped on it, now he has to sort it out.
Of course if counselling etc is on the cards you can work at it wholeheartedly. Do not rug sweep or minimise what he has done, this has to be dealt with first, then your relationship. It appears over the last three months he is weighing the pros and cons of having you and just keeping you as a plan B.
Tell him, you cannot live in this limbo land anymore, either you both get into MC now or he moves out and can sort his head out whenever he wants, but you may not be available if he decides to come back. Tell him you love him and would be willing to work on the marriage but that there must be 100% commitment.
Ask to have access to his pc, his phones, etc and put a VAR in the car in case something else is going on, do not sayin anything but keep your eyes open. based on what you have said it might well be he is in an EA if not PA.
Get yourself into IC to help you deal with your emotions, start doing the 180 on him (yes even now in the house) and just deal with domestic matters, no discussing anything about him, marriage, no pleading, etc. His current behaviour should not be rewarded so no sex, no hand holding, nothing.
tell your family and friends what you found on the skype, let him deal with the fall out of any, this is not your burden to bear, but his.
Move on with your own life, are you working? If not join a club, classes, gym, etc to get out and about. Show him that life moves on with or without him and you will not be sitting pining for him or waiting till he makes up his mind about you.
Later contact a lawyer and see what your options are. Be very firm and strong, you are not going to be your WH's Plan B. It is likely that when he sees what he is about to lose he will grow up. This is all counter intuitive but if you run after him, begging and pleading to work on the marriage, he will just keep doing what he is doing, having learnt nothing. There have to be consequences.