Even if you successfully completed the diversion, the case will likely appear on any thorough background check. Whether it will affect your ability to find work will depend entirely on the employer. The same can be said for the visitation question. If the other parent wants to make a big deal about your criminal history, it can have an impact. Retain an experienced family law attorney to assist you with a parenting plan.
The diversion will get the charge dimissed but even just a google search will turn up the arrest. You should disclose and explain and depending on who you are dealing with it could turn out well.
The arrest alone can cause you problems with both. Police reports and court files are public records.
The answer to your question depends somewhat on how the diversion is structured. In general, a diversion will be a lot less likely to affect you negatively than a conviction. The arrest won't actually appear on a lot of criminal background checks. However, if somebody does a thorough search they will be able to find it.
In my experience, when Felony diversions are offered on charges as serious as yours, it may indicate that they have a very weak case against you. This does not mean that you should necessarily not enter the diversion agreement. It means that you must hire an attorney, and thoroughly discuss all of your options, after a full investigation of the case. What you should not do, is rely on random answers over an Internet forum to make a decision as important as this.
Scott W Lawrence