Thanks. I should clarify.
I don't believe 50-50 access to be in jeopardy, but I am concerned about legal decision making (sole custody v. joint custody).
There is no reason to believe we wouldn't agree on medical and religious decisions, however, those related to which school the children willl attend could potentially arise one day.
With joint custody, your ex wouldn't be able to determine which school the kids will attend - you and she would have to come to some sort of agreement.
Do you really believe that your ex is incapable of providing informed input into decisions concerning schooling? Even parents who are incarcerated or hospitalized have had joint custody, because they are capable of understanding the importance of decisions affecting the kids and of taking part in these decisions.
Seeking sole custody because you think you might disagree with your ex somewhere down the line about schooling is not going to fly. Neither is seeking sole custody because your ex introduced the kids to her boyfriend. If you proceed in this way, you will look stubborn and petty to a judge. This strategy could backfire - if a judge is faced with two parents each of whom insists on sole custody and neither of whom will compromise, the judge is just as likely to award sole custody to your ex as to you.
If however you come in seeking joint custody with a clear parenting plan, you are showing that you are a reasonable and co-operative parent, and a judge is not likely to take custody away from you, unless there's some really pressing reason why you shouldn't have custody.
The way the wind is blowing, most custody arrangements end up being joint, unless one parent is really, objectively, demonstrably incapable of parenting. Much better to prepare for this outcome than to prepare for an outcome which you aren't likely to get.
ETA: It also doesn't really make sense to say that you're fine with 50/50 access, but you want to make all the decisions yourself. If your ex is a good enough parent to have the kids half time, why is she not good enough to take part in decision-making?