in addition to the good suggestions already made, i will add a little detail:
dont go on a "diet", but yes cut out the crap! cut out processed food and make veggies, nuts, beans and lean proteins your staples.
say no to "white": bread pasta rice etc!
say yes to: dark leafy greens (my faves are kale and rapini), raw veggies chicken breast, grilled tofu, beans, lentils, eggs (whites only if you're watching your cholesterol)
you want to be getting most of your carbs from veggies, as they are complex carbs, take longer to digest, and will therefore keep you feeling fuller longer.
say no to: lattes and fancy drinks! say yes to black coffee and iced coffees with sugarfree syrups for sweetener.
drink at least 2L of water a day. have it on you all the time, and add fresh squeezed lemon or lime juice to it. green tea and herbal teas are your friends!
if you're a drinker, kiss that beer goodbye! vodka and white wine/white wine spritzers are your friends.
eat 5-6 smaller meals a day or smaller meals with snacks in between. i always have raw veggies on me when i get a little hungry. when you are eating frequently it keeps your metabolism primed and burning. when you go for long periods of time without eating, you go into starvation mode and your metabolism slows down. also, raw veggies require more calories to process than cooked ones.
try to have one same meal a day: for me, i always eat greek yoghurt/cereal/berries in the morning. this takes a little guesswork out of the day.
think of your food intake throughout the day as an inverted triangle - you should be eating most of your food in the morning/day, and your smallest meal should be at night. dont eat before bed!
also: blended soups are your friend (ie chicken an veggie soup but half of it pureed). your body will take longer to digest a blended soup than a non-blended soup, and so you will stay fuller longer.
as for working out at home: get a skipping rope! jump rope with your kids. have races with them! dont feel embarassed!!! make it a fun game and involve them as well!
good luck you can do it!