I live in California and have been through a terribly bitter divorce and custody battles like you wouldn't believe.
For one thing, it's crazy to have a custody battle over a 16 year old. Here, children at 14, have a say in things. They don't necessarily make the decision, that is reserved for the court, but they take their feelings and the situation as a whole into account.
If you can prove this is a retalliation thing because you requested more support and IF your daughter is willing to repeat what her father told her, then you shouldn't have to worry about the custody part as long as you are certain that she does want to live with you.
How long have you known about this court date?
Did you file any papers in response?
In what manner did you "go after" him for more support? Was it through the court? Through the Department of Child Support Services? Was it verbal?
I have battled without an attorney many times and I never lost my kids. One thing I will tell you is that you cannot say you don't understand what's going on. Ignorance is not a defense. If you don't agree to what he is asking, YOU have to present something to the court outlining what YOU want. For instance, you request shared legal custody and sole physical custody with visitation as outlined: Then outline it.
I've raised two kids by myself. I understand how hard it can be financially, but to be honest with you, I was willing to have custody over money any day. $150 per month for a 16 year old is really nothing. I totally get that. But, unless you are certain you will receive a higher support award and he will actually pay it, I would tell him that you'll take the current support amount in exchange for you having full custody. If you are not prepared for an expensive fight, it seems like a logical solution. Your daughter is old enough to get a work permit, have a part-time job, she can make money babysitting, etc.
She will be 18 in two years. You have to weigh what you might gain, or lose, and if it's worth it for such a short period of time.
My ex husband dragged me through court so many times I can't even count. My son is 17 now and there is no more fighting. My son lives with me and sees his father as much as he wants. "Visitation" orders are pretty much out the window at this point. My son loves us both and has a relationship with us both. My ex pays a ridiculously low child support amount and although it might not be fair or right, by the time the court got around to making a decision about revising things, my son would be 18 anyway.
I don't know all the ins and outs of your situation, but I think your best bet is to ask for a revision in custody since your daughter has lived with you for the past two years and I'm assuming, she wants to stay with you. That part shouldn't be such a big hurdle. BUT, you have to complete and file the papers with the court. They can't grant something you don't submit. You do not need an attorney to respond to or file papers in your case.
You can ask the court for a continuance but it has to be based on something other than not having money or an attorney if you've had ample time to seek legal advice or file a response.
My area has Family Law self-help centers for people doing things on their own. You'll be at the courthouse tomorrow. Find out if they have any of those types of resources.
Hang in there.