Advice Please - Application Made Against Me

I have two children, age 9 and 14. 

For 9 years my ex partner and I have not been together and since that point I have paid child maintenance through a private agreement to her directly. That started out at around £350 per month and is now £430 per month. 

I have the kids Thursday through to Saturday (so 2 nights), collecting them from school Thurs and Fri and dropping them off at tea time on a Saturday. Sometimes they stay with me 3 nights.

I'm the only parent that drives so outside of my agreed days I also drop the kids off at after-school clubs, sports clubs, concerts etc, most of these being outside of my agreed days, which obviously costs me in fuel and time.  

I pay money into the kids savings each month and have done religiously for 9 years. I'm the only parent that does this; she has never put a penny into their savings accounts. 

I'm the only parent that takes them on holiday. As she doesn't take them on holiday I over-compensate by taking them on 2 - 3 holidays per year; usually a week abroad and then a couple of weekends in a caravan or tent in the UK throughout the year. 

Needless to say, like most dads, I also spend a fortune on my kids outside of child maintenance through treats, days out, clothes, uniforms for sports clubs etc. I even pay for my childs phone contract.

This agreement has always worked, there's not really been any animosity but quite clearly, having worked hard and been relatively successful in my career, I earn more than her. 

On the other hand she stayed on benefits for 11 years without a job. 1 year ago she returned to work 2.5 days a week in a shop and then only 2 weeks ago started an admin job full time. She lives in council accommodation where she hardly pays any rent (I think £100 a month), has discounted council tax, obviously receives child benefit, receives maintenance money from me and is now working full time. She doesn't pay for any maintenance on her house as it's a council property so they pay for the maintenance of her house.

On the other hand I have a mortgage, council tax, utility bills, car, and all of the other things that life throws at you. 

Only yesterday, completely out of the blue and with no warning or conversation, I received a letter from the CMS stating that she had made an application against me. I have 14 days to respond giving my income details. The income details they have put on the letter includes my annual bonus which is not guaranteed at all and fluctuates wildly from year to year. Their calculation, given my salary of £65k, is that I will now have to pay her somewhere in the region of £700 - £750 per month. 

The bottom line is that I simply can't afford that. I simply can't afford to almost double my child maintenance, whilst bearing all of the costs of life and all of the additional costs I take on outside of paying her the current maintenance. 

I messaged her asking why I'd received a letter saying she was making an application against me; to which she has ignored it.

I feel completely shafted. The only way I can see being able to afford it is to stop putting money into the kids accounts, not take them on holiday and stop doing all of the extra things I do and pay for; but the only people that is impacting is the kids. If I turn around and tell the kids I can't afford to pick them up from after school clubs anymore then she won't do it (she cant drive remember) so the kids lose out.

Any advice from similar situations would be welcome. At the moment I can't see how I'm going to be able to afford to get through the next few months.