Hi there! Welcome to Oklahoma! :) We live in Norman so I am not very helpful about Altus.
But I can tell you about OKC and Norman. I had my 2nd baby at OU med center. After a planned homebirth with my first that we had to transfer to the hospital for (this was in Montana) and I had severe postpartum hemmoraghing, I decided on a hospital birth for my 2nd. Anyway -- long story short, I had a beautiful, all natural water birth at OU. OU Med center is known for its wonderful CNMs around here. I used Anne Stewart -- but she has since retired. Lots of moms have had beautiful, natural births and water births there (they will tell you that you can't plan on a water birth but if you are in the tub they aren't going to make you get up I am told).
As far as homeschooling, there are lots of groups around here. Depending on what you are looking for -- there are religious and non-religious groups. Oklahoma is a super easy state to homeschool in. You don't have to do or prove anything to anyone. Around here, lots of people homeschool for religious reasons. If that is not what you are looking for, you will have a slightly harder time finding a secular group. But they are out there. :)
A friend and I started Norman Secular Homeschool Association about 5 years ago. It has grown LOTS since then and we have lots of activities going on. We also have a sister group in Edmond (called Edmond Secular Homeschool Association).
Norman has a very active API and LLL group. There are also other LLL groups in OKC too.
I don't know much about doctors in OKC. But I can tell you to be really careful with pediatric dentists. For some reason around here most of the dentists do not allow parents to be present during exams after the first visit. :( This boggles my mind and I never encountered this before moving here.
Good luck with your move! Drop me an email if you end up in OKC. I have two kids (8 and 5), we are anti-vax,anti-circ and also homeschool.