You won't find many sympathetic ears on this forum... If the question was "how do I extract more money out of my ex" , you'd be on the third page of comments by now.
The CMS are legally obliged to count your dependant children, however the discount you get for dependants at home is pretty pathetic.
I'm not entirely sure what formula they use, I think I heard that they disregard the first 11% of your partners income when calculating his CM liability, but that may be wrong.
I've heard of many cases, and in most cases the reduction for dependants at home varies from £5-35 per month.
Which I think is absolutely sickening, considering the amount paid to the Non-resident children.
You are correct in thinking that you effectively get "stung twice" as a "second" family.
You have to 1) Pay CMS (12-20% of his wage) and 2) Lose out on an equal amount of tax credits afforded to "first" families. So you as a second family, and most importantly, yourself and your children are paying out twice... Actually three times if you are both tax payers to begin with.
Unfortunately the CMS think it's okay to throw "second" families into poverty, all whilst throwing vast amounts of money at "first families" or single parents.
The CMS are ideologically opposed to treating "second" families in the way that they do "first" families... Because in their extreme world view, only the parent with the children is entitled to a life, and the Non-resident parent is not entitled to a life... I personally, think it's part of an extremely subversive and dangerous agenda.
I suggest you start running the maths and know well in advance if you can afford to pay the bills in future or not.
I suggest you join the Non-Residency CMS Facebook groups, where you will receive a better listening ear & solid advice.