Yes the courts always favor the mother and you basically have no rights, however you are in the position many mothers letthemselves get into which can work for you. You need to do what a mother would do. Much more so because if you do not you will get really fcked over. You let yourself get into a position where you are not earning enough to support yourself and you have the kids to take care of. If you were a woman you would be "entitled" to clean your hubby out, but because you are the hubby you are going to have to go uphill and prove everything or you will get cleaned out, lose your kids, and be struggling to support someone that earns plenty for the rest of your life.
Listen carefully. Verbally agree to whatever to keep her from getting angry. You need to get a lawyer, a good mens rights one immediately. Look at martindale.com or search. See several for 1/2 hr. first consults. Find one that feels confident you will get primary custody! Don't try to save money now or you will regret it the rest of your life. Don't try to save anything because she will be walking away with half or more of anything she can identify soon.
File for divorce immediately. Ask for primary custody of the children and she gets liberal visitation. Ask for temporary posession of the house and child support from her on an emergency, retroactive, and ongoing basis until the kids are 18. Ask for support along the state guidelines with your income considered and include child care expenses. She needs to get less than 40% in most states or you will not get enough money from her to take care of the kids on your salary. CS goes down drastically at 40%. You can informally let her have them more than 40% after the fact, let her know you'll let her have them as much as she wants but will only agree to 40% on paper. Ask for spousal support to pay for the ongoing housing expenses, have your bills for the past few months ready to show to the atty. and totalled. Show you take care of the kids and you need $ to keep on doing so. Gather all the proof you can and witness names and addresses that you are their primary care giver. Begin looking for a better job or getting retraining info/costs, but don't do anything different until it's final. Do everything very quickly before animosity sets in. See if your lawyer will review a mediated settlement, or do a collaborative one. Be sure to ask for the attorneys fees in your filing, she has the financial ability to pay for your and her attorney and the ability to win a pissing contest with you, ie: pissing away all your funds.
If she is reasonable and willing to support you for a few years while you get self sufficient, and pay for the kids and all while she goes slam dancing then you'll be lucky to get away with a mediated settlement for a few thousand. What I could see happenning is she won't like to step up to her responsibility and when she finds out what it's like to be in what is normally the fathers position, (up to 60% of her paycheck goes to you, she gets EOW & a few nghts a week)she will become adversarial and try to use all the tricks built into the system to "protect" women. Again: DON'T get her angry and try to get this over as quickly as possible. Don't be angry, the best thing that could happen to you is she finds the pierced BF of her dreams and moves out. Good luck!