I'm sorry, but "I need space," in my opinion, almost ALWAYS means "I need space in which to conduct my affair, unencumbered." That being said, you still have to give it to her -- but you DON'T have to pay for it, and shouldn't.
Stop pursuing her -- no begging, no pleading, no ILYs. See if you can get her to agree to 100% no-contact, and full transparency, during your time apart, and go to a good family therapist with you. If she won't agree to the transparency, and accuses you of being "controlling," then tell her you will proceed under the assumption that she is having an affair, and will make moves to protect yourself accordingly. No yelling, no ranting and raving -- just businesslike.
