How should I go about writing an appeal? Should I discredit the other party and their statements?

Dear ?,
An appeal is not about the facts. It is about the law. If you believe someone lied, you cannot argue this on appeal. The credibility of the witnesses is a matter for the fact-finder (here the ALJ) and his/her decisions as to what the facts are cannot and will not be reviewed by any higher court.
You can appeal if there are errors of law by the judge which prejudiced your case. It seems clear you do not have enough training or experience in law to be able to recognize any errors of law, much less those which one could possibly convince the judges on a reviewing court were prejudicial to your case.
You need to have your case file reviewed by a good local Washington family law attorney with experience in appeals. Only such a counsel can give you an opinion as to whether you have any chance on appeal. Probably you cannot afford to pay such a counsel. So you need to find out if any legal aid societies will do family law appeals pro bono for you. If you contact your State Bar, they should be able to help you find this out.
Yours sincerely,
Tim Provis
Cal. Bar No. 104800
Wis. Bar No. 1020123