I sympathize with you, C.. My aunt was married to a man who had a child from a former relationship. In Pennsylvania, I know that the court's give preference to the first child(ren). It did not matter to the court's that her husband had three children with her. It did not make a difference in the amount he was required to pay to his first child's mother. Supposedly, the court's would look at your ex's income. They would allow a certain percentage to him to live on each month and then determine child support payments from what is left. The court's can determine he must pay up to 100% of the remaining amount (after they take out the percentage he is allotted to live off of). I'm not sure how they determine how much is actually appointed to the parent with custody. I don't know if it is determined by number of children or what after that. I do understand though that the biggest factor in determining the amount of support is his income.
Don't feel guilty about taking him to court for more money. He chose to have children with you. Additionally, he knew he had children with you when he chose to have a new son with his new girlfriend. His new girlfriend knew about his other children as well. You are not taking anything away from them. They knew about their responsibilities when they chose to have their son. You have to do what is best for your kids. Your kids need to have quality care while you are working at your job.
Also, while you are working on getting more support, you should look into different programs that might be able to help you meet your needs. I know in the Allegheny County area, there is a program called Childcare Partnerships. I don't know what your income is but it provides assistance with childcare and if you live in the area, you might be eligible. If you live in a different area, check the area you are in. I know that the Childcare Partnerships programs received part of its funding from the Federal Government so there are probably similar programs in other areas.
Good luck.