I've told my story a few times on here, but if it helps people I will tell it again. My situation is very close to yours so I will tell you what has worked for me.
I, like you, have 2 small kids (3 and 16 months,) a full time job at a small public accounting firm which doesn't pay for any of my study materials or tests, and I just graduated college barely over a year ago. I went back to college when my wife told me she was pregnant with my oldest child when I was 32, so I am an older candidate (just turned 36 two weeks ago.) In 4 short years I have had two kids, completed 4 years of college coursework in 3 years while working 2 jobs, started a new full time public accounting job that has included two busy seasons, and managed to pass 3 exams all on my first try. If everything goes according to plan I should pass AUD in 13 days and be completely done. Here's how I did it.
First, your husband/wife/partner has to be on board. If that person isn't 100% behind you it won't work. When you tell them you can't help with the kids this weekend because your exam is in 2 weeks and you need to study, you are going to need someone who is OK with that. My wife also works full time as a nurse – so she works 3 twelve hour shifts a week. It helps that she has 4 days off per week to deal with the kids instead of a normal 2 day weekend. We are also extremely lucky that both of our parents are retired and willing to help with the kids, which has helped a ton for being able to find time to study when I really need it. But here is my daily/weekly routine for studying using Becker.
I follow the Becker study plan and do one unit per week. This usually works out to be 1-2 modules per day depending on the size of that particular unit. I try and plan it out so I can get the unit done in 6 days instead of 7 so I can have Sundays off to spend all day with the wife and kids, but this isn't always possible. Sometimes you will need weekends to catch up on studying you couldn't get done during the week. My wife knows that at 9pm every week night that my butt will be in that chair at the kitchen table studying until my studying for that day is done. I can't stress that enough. You need to set up a boundary that your study time will start at a certain time each day no matter the circumstances, and you need someone who understands that and can deal with it. Sometimes studying can go until 11-12 at night if it has to, but it gets done. A typical day for me goes as follows: Wake up at 6:30 – get ready for work, work from 8-5, come home – help wife feed, bathe, and put the kids to sleep. Usually all this happens and the kids are sleeping well before 9 and then I study. Rinse and repeat. But as I'm sure you know sometimes one or both kids are being difficult/sick and aren't asleep by 9. My wife knows I have to bow out so I can study and she takes over. It's not always easy.
The tips I can give you are this: take one day a week to sit down with your partner and plan out your meals. The crock pot is your friend here. There are a myriad of cookbooks that can walk you through easy to prepare crock pot meals that you can put in before you go to work and come home and have a hot meal waiting for you, the wife, and the kids. This will alleviate the problem of having to worry about dinner for everyone most days and will help out more than you realize. Even if your plan is simply “Thursday we'll just order pizza” get that stuff out of the way as much as you can. The last 2 weeks before I go in to take an exam are my review weeks. I need all hands on deck and I basically let everyone know that I will be studying as much as humanly possible and no one can expect me to help with anything. If you communicate this with your partner before hand it will allow them to make other plans to get help with the kids. My wife basically moves back in with her parents with the kids for 2 weeks while I'm reviewing leading up to my test. It's not ideal, but if you give your partner a 6-8 week heads up before you basically kick them out of the house for 2 weeks, you can usually make it work.
The final pointer I can give you is this – you have to want it. It is never going to be easy to pass the CPA exam. Trying to do it with kids is harder, yes, but it is doable. Many have done it before and many will do it after both you and I pass. I don't think waiting until the kids are a little older will make it any easier or harder, really. The thing that will allow you to pass is making up your mind to pass and following through with it even when it gets tough. There are tons of examples on this forum of people pushing through tougher odds than having kids to get the test finished and some of them are a good read when you are feeling down and need a pick-me-up. If you want it badly enough you can make it happen.