finz, you are sounding weird and hostile. She is having trouble getting the man to communicate about important parenting issues within a reasonable timeframe or at all. Her attempts to contact him and initiate the conversations are responsible parenting.
OP, if there's a mediation clause in your decree, use it. Bring him in to discuss the issue of passive-aggressively ignoring the texts. Decide on a range of parenting issues that require his cooperation and agree to it.
If you can't do that, document your efforts to involve him, let him know that you must make decisions if he will not reply, and then make the decisions on your own. If he challenges them later, you have the documentation showing that you tried to work with him but he refused to answer. I would suggest using more than one means of communication for making the requests -- if he doesn't answer texts, email and/or call as well with a notification that you will be making a decision by [deadline] and you would appreciate having his input, and that if you do not hear from him by then you will assume that he is fine with whatever decision you make. Send a copy of the message to your lawyer.
As for activities, if he's unreliable about transportation, arrange the transportation on your own and schedule them for your time with the kids.