I don't know your Dad, but keep a log of your exercise, and your weight. And, demonstrate your behavior change and new lifestyle when you do see him.
Maybe he would be willing to contribute toward exercise equipment for your birthday or Christmas?
If that doesn't work, revisit the topic regularly. If he sees the change in you, he may change his mind.
And - trust me - working out at home without a treadmill does work. If the video you are using isn't enough, supplement with others. You can even find good workout routines free online
And - if you have cable TV, on demand has some good stuff too.
Most libraries have videos to check out as well.
I know you are disappointed, but don't let this setback get you down. There are many chickies around here (not just me) that have lost weight and gotten fit using just the basics.