If my wife files for a divorce and I fight it because she is not divorcing me for adultery and the courts gives her her way, am I not allowed to remarried even if I fought it and was force to allow her a divorce?
There is only one exception given that allows for divorce: "And I say to you, whoever divorces his wife, except for sexual immorality, and marries another, commits adultery; and whoever marries her who is divorced commits adultery" (Matthew 19:9). Even here, the exception is in the implication. Jesus states that divorcing and marrying again is adultery. The one exception is a divorce because of fornication on the part of the spouse.
For thousands of years, divorces were granted because the one who filed proved that the other spouse was unfit. Because of the need for proof, divorces were rare. When no-fault divorces came on the scene, the need for proof was removed. It was deemed sufficient that one spouse wanted out of the marriage. Hence, what is now common is to see the spouse guilty of adultery filing for divorce in order to justify marrying his or her lover. Because of this, I don't see who initially files for the divorce or what is written on the divorce decree to be significant. The question is whether the cause of the divorce was because of adultery on one spouse's part. If so, then the other spouse has a right to remarry. The adulterer does not have a right to remarry because God continues to hold the adulterer to the terms of the covenant that he or she made.
There is no allowance for remarry if someone refused the divorce. I agree it is hard. The disciples found it hard. "His disciples said to Him, "If such is the case of the man with his wife, it is better not to marry"" (Matthew 19:10). However, all covenants, including marriage covenants are serious matters. They are not lightly broken and so should not be lightly made.