This is a great thread!
For more info on HIIT go
here
The good news is that you don't have to spend too much time getting good gains.
I do a modified 'cross fit' type routine at the gym. Cross fit is good because I find it interesting and varied, requires full body movements and it is over quickly (the bad parts are that the people who do it are fanatical nutters who think overuse injuries are a badge of honour and eat far too much protein for my liking)
For WOD (workouts of the day) go
here
It is important to get out and do your exercise - don't think that you are being greedy. For one it helps your mental health as well as physical health. Two: it is an awesome example for your kids (they will love you no matter, but it is so much cooler not to have the 'fat' dad). Three: you partner will also think you are much cooler
As a mum myself I do not begrudge my partner getting out for his exercise time. I do it myself