FDS

It might be easier to get into Berkeley than UCLA, in that Berkeley is not known for African history and you would have much less competition than at a famous Africanist program like UCLA. If Richard Roberts is still accepting students, you should consider Stanford too.

Honestly, you can handle it if you want to. My mom started her PhD after having me (I'm the youngest of 3). Did it take her longer than some of peers? Absolutely. But she finished and had a career based on her doctorate outside academia. I would be clear with prospective advisors that you have a family and gauge their reaction (if possible through an in person conversation if you're near there anyway). That way, you know if they'll be understanding/supportive. If they aren't, then it will be very hard to be successful and actually complete the PhD even if you do get in.

Make sure the advisor you want to work for at UCLA is taking students for the year you’re applying to. I find that making sure there are advisors who would fight for your app at a particular school is paramount.

You'll want to express your research interest in terms of a specific historical question or questions that you are seeking to explore. You also want to start thinking about sources, if you haven't already. Have you read Graham Furniss' work? His chapter on Hausa print culture in Karin Barber's edited volume Africa's Hidden Histories might be useful for you.
By the way, Bruce Hall at UC Berkeley would be an excellent adviser for your interests. 

I second the above advice--reach out to potential advisors and see what they say (though note that this is an extremely busy time of the academic year for a lot of profs). I'd be careful about saying you're only interested in UCLA (as in, I wouldn't mention it at this stage--regardless of your circumstances it will make people think you're not genuinely committed to doing "whatever it takes" to try and succeed in academia). But it is definitely worth being upfront about what you've been doing since your MA and why you want to do a PhD in history--what is your MA in? Plenty of people (not the majority but plenty, even so) come to a history PhD from another field, but pretty much all of those people have a good sense of the historical field that they're entering. The language is a huge advantage but do you also know your way around the historiography? I am guessing that you probably do, but it would be something to make pretty obvious straight away, because it's common for people to come to history thinking that it's about "uncovering the past" etc etc, when it's really about engaging in/complicating/messing up whatever contemporary conversations are happening, and it's good to be able to position yourself somewhere inside a conversation, even if tentatively. Good luck!

You have the credentials. The most important element of your application, however, will be how well you articulate your fit with a potential adviser and your research interests in your SOP. In African history, it is less important to find advisers who would work on your specific sub-region than it is in other fields, but you should be able to make a strong case at least for shared research interests. What are you interested in and who do you want to work with at UCLA?