Hi,
Any weight loss program - and any training program - have to be tailored to your specific needs, and you should discuss this with your personal physician before you start. Especially in your case: if you just had a baby, you and your doctor have to take into account the effects of hormones, breastfeeding, sleep deprivation, etc.

OK, now that we got the disclaimer out of the way... here's my two cents - but keep in mind that I am NOT an expert at all!!! So really these are just random ideas and suggestions.

One way some people use to lose weight is to try and increase the weekly mileage but maintaining a constant average calories intake.
For example staying on a 10-14 calories/lb/day intake, and at the same time adding 5-7 miles per week. If you ride let's say four to five days a week, you could try to make each ride 1-2 miles longer every week.

Likewise, you can try to work on your riding style to burn more calories. You could add some speed work to your ride. So, instead of just roll out easily all the time, you can add a few intervals at higher speed. Or add some short heavier efforts, like power climbing, or sprinting, to some of your rides. For example let's say that on a given day you decide to ride ten miles. You could use the first 3-4 miles as a warmup, then do 3 miles like a TT, keeping the highest constant speed that you can keep, and then go back to a recreational pace for the last three miles. On another day, you could pick a few landmarks on your route and decide that as soon as you reach those landmarks, you are going to sprint out of there and go as fast as you can for like 30 seconds, or 45s, or 60s. On another ride, you can tackle a few hills and decide to include some variety in your climbing. For instance stay away from the smaller gears on one of them and power climb; then approach another hill at higher cadence sitting down all the time; and another changing gears and moving in and out of the saddle to keep your speed up. There are many ways to introduce a little bit of heavier training in your daily rides.

Of course the best suggestion (after the #1 to discuss this with your health care provider) is to work with a coach if you can find one in your area. If you can't find one that is able to work with you, try asking other cyclists about local teams - racers often have access to a coach and can point you in the right direction. If that is not available either, you could try to attend some beginner training clinics and see if you can get some personalized suggestion from the trainers.
Some people also offer long-distance coaching (Carmichael does too I think) and they may be able to help prepare a training/weight loss program for you.
The least interactive option is to read and learn about training, it's not as good as dealing with a trainer but is still better than nothing. There are several books about training - and some are specific to cycling, like those by Armstrong, Carmichael, Burke, etc, there's really many out there.

And there are many people here on the forms who race, train, and coach... so they can probably give you lots of good suggestions!

Best of luck, and keep us posted on your progress!!!