Istanbul Tea, I'm another who's right there with you.
2.5 years ago, I was 280# (for a 5'5" woman, that's pretty big) and hadn't ridden a bike for 10 years. My wife and I decided we needed to go car-free and for that, I'd need to get into riding shape. I started out on a stupid garage-sale exercise bike -- well, actually, just its pedals as I sat on the couch -- pedaling for a minute or two at a time.
Six months later, we sold our car and bought our bikes. The ten-mile ride home from the bike store was the hardest work I've ever done. Way more than either of us were ready for.
Now, I can do short-distance commuting (10 miles a day, 4-5 days a week) or a longer trip (a 26-mile round trip once or twice in a week) but not both in the same week. I've lost some, but not a huge amount, of weight (I was 247# last I checked). My clothes fit me a bit looser but I haven't yet needed a whole change of wardrobe.
But I didn't get into it to lose weight. I did it, in part, because I didn't like the way I was starting to feel in my increasingly sedentary life. I know I'm stronger because hills that used to kick my butt (lots of stops to recatch my breath and let my heart slow down and my legs quit burning quite so much) now only knock me around a little (I can climb them without stopping if I go slowly enough).
I'm lucky in that my wife, who is athletic but had fallen out of training, is a patient soul who is content to go slowly with me. As your own wife says, you'll get there. Just do it at your own pace. Any who would discourage you or disparage your efforts aren't worth a second thought.