Why can't my wife workout at home?

Okay, so my wife and i just had our first baby about a month ago. My wife, now, is feeling like she would like to get back into a regular workout routine- Which is perfectly fine with me. The problem is she insists on getting a gym membership to do so. Now, the gym membership is only $20 a month so in that regard it's not that big of deal. My problems primarily are 1) she can't drive herself- she hasn't gotten her license, so it would turn into a nightly routine of having to take her down there, wait for two hours, drive back, not have her around to feed the new baby, etc, etc, and i think it would be more hassle than it's worth. My 2nd problem is that we are on a pretty tight budget right now, and $20 bucks plus gas is just money that we don't need to spend. When i pointed out that the best exercises for her particular situation (jumping rope, crunches, jogging, stair steps) can all be done at home, and will burn fat, and tone her postpartum belly and thighs as-well-or-better-than-the-gym, she accused me of not being supportive, and not taking ample concern regarding her desire to be fit and lean. Furthermore, she insisted that, as much as she might want to, jumping rope is impossible for a breast feeding mother. I, not being a woman, cannot answer this, but surely she is not the only large-chested rope-jumper in the world. Right?