Don't be so hard on yourself. The kids probably thought it was great having popcorn and jelly beans for dinner!
I was thinking about the Mitch situation and how it is tough being a single parent - especially when the kid are attached to an absent parent. In my case, it will be easier - there is no absent parent to explain away.
I don't know if this works in personal R's... But at work, when I really need someone to do something I know they don't want to do, I have learned to tell person what I want them to do acting "as if" they will agree to do it - instead of inviting discussion. I find when I invite discussion they either ignore the email or come up with excuses to wiggle out - and I find myself on the defensive. I also keep it short so my message doesn't get lost.
For example, sending an email to Mitch saying, "Congratulations on the JH position. (setting a nice tone) We will need to adapt to this new development. (justification using we language - as in we are on the same team) Please make arrangements so that the kids can fly to Mass and spend on ___, ___, ___. (Driving it home short and sweet - in a manner that assumes agreement - shifting the burden onto him to disagree or confront) Please let me know if you have a problem with this otherwise I will work on scheduling ___, ___, ___. (Decision is made unless he disagrees). Add a few extra dates in addition to what you think is right, so that it looks like you are giving if he whines about not being available on those dates. If wants to change the dates - you have already made plans and are unavailable - no need to elaborate on what those plans are.
This is just an example of the tone. I know you have already discussed some of this with Mitch.
You are a great mother. Everyone needs down time. I am sure you are great even when you are tired. You are your own worst critic. Mitch is leveraging being able to count on you picking up the pieces when he drops them. This may be a way to create a situation where the kids see their father and you get a chance to recharge your batteries.