These are terrible feelings to be having but a few things to note from your post:
* Idealized= you probably nailed it with that statement, it is good that you can recognized that. In the future discuss your vision with your family. Don't let it bother you, if at the end of the run, they were happy and you all got a run in, that is worth embracing. Find your happiness for their achievements, and think back to how far you've come since your injury.
* 6mile pace should be different than your marathon pace- depending on your training this could be why you have endurance and not speed.
* Think about your training load. What did you do the day before or even hours before this run? Is your family also training for an Ironman? (the could be fresher than you are, they may also not have to get another work out in anytime soon, and your legs could be heavy from your training load. Don't be so hard on yourself, think about possible reason why you felt that why; especially if it is not indicative of your prior trying sessions. Hydration/fuel could play a part).
* Holiday= emotion, stress- breathe, it will be okay. Sleep, fueling are usually off during this time period.
* 4 years commitment to this race, do not let a bad day take away all of your effort. Say you are not where you want to be,acknowledge that. Now, think about what you need to do, to get to where you want to be, you still have a few months to put in some steady healthy work. Focus on getting one day at time done, not the overall goal.
* Respectable Time- Finish an Ironman is respectable. Hard is hard, no matter how fast you go, everyone is struggling with their own efforts. Believe in yourself, and just keep putting one foot in front of the other.
* Be nice to yourself, you are courageous for attempting this, even professionals do not show up at every race on top. You and your family will be proud of you by showing up to the line, for fighting for a goal you wanted.
Congratulations on having a family that can run, and that was willing to run with you even if your mad you couldn't keep up, let it motivate you to keep working for your goals.
Try to find the positive in your progress, if you accomplish what your not sure you can; you will be amazed at the confidence it will bring you in so many other parts of your life.
Keep at it girl, I am cheering for you!!