Postpartum Exercise class, baby/toddler friendly?

Yes! I love mama army stroller fitness classes. It's a great workout and the teacher, Angela, modifies everything to your level. I bring my 4 month old. She loves being outside and being pushed around in the stroller. Here's the website. She also has a Facebook page which she updates frequently.
http://mamaarmy.com/location/

The Bar Method in Berkeley has a daycare. I believe it costs an extra $5/class.

I would strongly recommend the Dailey method on ashby! They have Dailey baby classes tuesdays and Thursday's where you work out with your baby in a carrier. I think they say babies up to 7 months but not sure. They also have childcare very frequently for $6 during a large amount of their classes as well. I've been going for a year and a half, before baby, pregnant and after and swear by the Dailey method!

Mama Army! I started a couple of weeks ago and LOVE it! I never thought I would be looking forward to working out XD. The trainer, Angela, is amazing and the one hour workouts are always fun. Babies and tots have a blast too. I can't recommend her highly enough. 

Ps. The first class is free! 

http://mamaarmy.com/

I really enjoyed my recent Mom & Baby yoga classes at Then Comes Baby in the Grand Lake neighborhood of Oakland, which was easy to get to from 580 coming from Emeryville. With the help of the baby holder I was actually able to have enough time to myself to work up a little sweat (though that wouldn't take much these days).  The baby holder was super-sweet. I thought at first that I'd be nervous having someone hold my baby, but it's a really intimate and friendly environment, so it felt more like being with new friends.  Torrie really did a great job teaching the class and I enjoyed it enough to try out their other class later in the week, with a different instructor (Alexa, maybe?).  Then, afterward, it was nice to hang out and feed my baby.  The baby holder even brought me a cup of tea!  They were really great and uber-accomodating and probably would be okay having an older baby there.  Here is their site: http://then-comes-baby.com/yoga-dance/

I took Karen Casino's classes after both of my boys were born -- it's been years, but looks like she's still at it:  http://www.karencasino.com/blog/ .  Great classes for reclaiming your abs, regaining some core strength, being with other new moms, and getting out with little one in tow.

No relation to Karen, I promise.  Enjoy!

I go to some pretty great stroller fitness classes at Live Oak Park with Angela of www.mamaarmy.com

the classes are infant and toddler friendly, open to all fitness levels, and really fun. It's a great group of moms. The website has all the info. Or just stop by Live Oak Park Monday-Thursday 9:30 or 11:00 am. To try it out,  first class is free!

The Lotus Method is opening it’s fourth studio this March on Piedmont Ave. in the Easy Bay. I started with them when I was pregnant at the studio in SOMA near my office and plan to continue once the Piedmont studio is opening. You can bring your baby to the sessions. www.thelotusmethodsf.com

There is an awesome bootcamp in Berkeley called Mama Army Stroller Fitness with Angela Warren (http://mamaarmy.com/). It meets Monday-Thursday and Saturday mornings. There is also another baby bootcamp in Oakland at Lake Temescal with Mary McQueen which is great (https://babybootcamp-alamedaoakland.frontdeskhq.com/schedule#/month?dt=…). It meets Monday-Thursday mornings at 9:30.  Both of the instructors are really great and always give modifications. You can workout at your own pace. The other moms are also really friendly.

You should totally check out Mama Army with Angela Warren.  It's a super fun outdoor body weight focused strength and cardio and abs class designed specifically for new moms! She offers 2 classes each day in Berkeley at Live Oak Park, one at 9:30 and one at 11.  Babies and toddlers welcome. Bring baby in stroller, and even a playmat is also fun on nice days! For mama, don't forget a yoga mat, a resistance band if you have one (Angela has extras if not), and water! And expect to work up a good sweat! Drop in or monthly membership available.

www.mamaarmy.com

Mama Army! We get together on Saturday mornings at Berkeley Marina & my daughter has really enjoyed it when we've gone. 

Just wanted to second the Mama Army! Angela is a really high level, elite athlete who is also incredibly warm, compassionate, and committed to creating a wonderful community of moms. She will get you in fantastic shape, and you'll also get to meet a really caring group of other moms. In addition to organizing workouts, she sometimes organizes playdates for the moms and kids as well, and it's a great way to get to know others. Highly recommend it!!! http://mamaarmy.com/location/ and https://www.facebook.com/mamaarmystrollerfitness/.