As a person who also has a family, I actually also want to try to give up gambling, even though I have been doing it just for fun, but I also realize that there are big risks waiting for me ahead, so that's why now I am starting to set strong limits in my gambling activities.
I think what you're doing is excellent, don't forget that the most important things are that before playing you establish how much money you can be willing to lose in a game session and if your budget says or dictates that you can only lose but 5usd then that is the only thing you should lose, in case you manage to increase it then withdraw it, there is no other way, it is better to do it that way because only then will you be able to make yourself more suitable, but it is necessary that you apply my technique, but yes, there are times when you do not have enough money and you have to respect when you have those limitations.
Having a family and also being an active gambler could be one of the most antagonistic things one could think of when comes to personal finances and planning for the future, if you asked me. I believe the thought of wanting to step down one gambling budget is natural and even wise, for the sake of one and those we love,.but one does not necessarily needs to completely give up gambling in order to be a responsible parent, in my opinion. It is about keeping the budget, as you mentioned and not allowing greed to tempt us to wager more we can afford to lose in a single session, otherwise there is where the problems start for all the family members.
If I ever decided to start a family on my own, I will indeed reduce my time dedicated to gambling, but I won't quit completely, as this sector of entertainment is very intereting to me.