Lacking time and motivation

I'm in a somewhat similar boat. I have two kids; one is 2 months old, the other 2 years. What I find helps is writing daily to-do lists the night before. I'll admit that I'm almost always tired, and I don't always complete my list. I do at-home workouts and I run the length of my apartment every other day, because I can't afford a baby-sitter right now.

You don't need to work out 2 hours every day. I get a 45-60 minute workout in on my run days, and about 30 minutes the other days with a rest day each week. A good portion of weight loss is about diet. You want to have a caloric deficit, but you also want to eat well for your body. If I consumed less carbs, I'd probably be a little less exhausted on a daily basis lol

While I will be the first to applaud getting your exercise plan going... You will be better able to manage weight by first controlling your dietary intake.

My personal approach was to begin by using MFP to log everything I ate and everything that I did as 'exercise'. Seeing that I was over-eating (and under-exercising), and where those many failures came from allowed me to lose a large portion of my weight without modifying anything more than my eating. I found that eating a bit more in-line with my body's needs helped me to conserve both time and money compared to how I'd been eating previously, and in the time savings, I was able to fit in a progressive resistance exercise program to help preserve my muscle mass as I continued to lose weight.

While it would be great to have a world full of extra-time and supportive like-minded friends, the only thing/person that you have absolute control over is yourself. If you modify and manage your eating, you'll find yourself miles-ahead of trying to add exercises to a busy life and habitual over-eating.

Overly simplified: It takes only an instant to "not open" a candy bar, or you can eat the candy bar and then try to burn-off those calories with 20-40 minutes of exercise. Easier to eat properly, if only as a time-saving measure.

I always recommend that as soon as you're getting on top of your eating (including sufficient protein, of course), that you try to add progressive resistance exercises to help you maintain muscle... remembering that weight is a measure of your entire body, and too many people find that they've dieted-away some of their muscle because they were fixated on the scale and not the condition and sustainability of their body.