There are four things on this thread that have horrified me:
Firstly, the frankly Dickensian attitude that some posters have towards adoption - the idea that there are different ranks of importance in one's children and that birth children are/should be more important than adopted children. Also that there are different ranks of adopted children, with known-child adoptions being less worthy/important/valuable than unknown-child adoptions. There is also a sub-text here that people outside of the parents get to decide which of the parents' children are their "real" (most important/worthy children).
Secondly, the idea that a person shouldn't live their life a (legal) way that makes them happy, in case it has a knock-on for people who may inherit from them. Everytime the OP's ex goes on holiday that is money that could go towards the OP's child's inheritance. Should he not go on holiday to protect the OP's child's inheritance? If he falls off a horse and breaks his back he could end up using all the inheritance to pay for his care needs. Should he never ride a horse (or ski? Or go rock climbing?) If we applied this principle across the board nobody would ever have second children, or certainly not children from second relationships.
Thirdly, the idea that anyone (including someone's ex partner and their adult children) have the right to have input into whether somebody who has been a good parent goes onto have further children or how they have those children (assuming there aren't more general ethical issues to the method proposed). How someone becomes a parent (again) is nobody else's business or concern (and in fact adopting a step-child is in many ways less risky for a birth child, as the step-child is a known factor; who knows what needs/personality a further birth child could have).
Finally, the idea that parents of adult children shouldn't do things unless they advantage (rather than "don't cause direct harm to") their adult children. When my children are independent and full-grown I fully intend to do lots of things that have no advantage whatsoever to my then-adult children. In fact if you take a long term view some of them could be seen to have a detriment to my adult children as my travel plans/possible hobbies will certainly eat into their possible inheritance.