OP I'm not clear on what you're asking exactly.  You have a plan to use your dad's stock farm, sounds like, for part of the livestock management, and I'm guessing you understand livestock management if you grew up around it, which means you also know it's not quite as simple as just "throwing the heifers in with the bulls"--that's good for part of the year, but at some point you'll want to move them, if you're going to manage them well,  which I'm sure you also know.  You may well know more than I do about that.

So..."How many cattle can I keep on 9 acres" is a really open-ended question.  

I saw no mention of a barn or hay or supplemental feeding, so...
Give us more information.

Editing because I missed part of what you said in your original post.

So...:  Are you talking about putting the heifers in with your dad's bulls for breeding, then bringing them back home?

Are you gonna fence the whole property? Or pastures in the open areas?

Or what?

OH...and CONGRATULATIONS!  That's a beautiful piece of land.

That's really awesome.  Good job.

I predict you'll need a separate little area for the milk cow, but you might not.  This begs the question..."Where are you going to milk her?"  You'll want to keep her close, and you need a structure that's warm and dry for this, as you really don't want to be sitting out in the rain milking, and if it gets cold at all, milking with cold wind and rain blowing around you is about as miserable as it gets.

You have a couple of options:

1-Sell her calf as soon as it's old enough so you get all the milk.  (I can't do this, but you might be able to.)

2-Keep her calf, which eases the need for milking, but does not take it away, if she's a good cow.  (The calf won't take all of it, at least early on.)  This is a good situation, because a BAD situation is ending up with not enough milk for the calf, which means you'll be bottle feeding to get it strong enough to sell both of them.  So you'll end up figuring out how much milk she gives, taking some, but making CERTAIN to leave enough for the calf.

You will also run into having beef calves who are getting weaned, bugging the crap out of the dairy animal to try to nurse (not always, but it happens) so it may or may not become necessary to separate her.  I predict you'll need a little shelter for the beef cattle in bad weather,  especially winter (assuming you do get some winter down there).   You've already thought of that.

You might not need two depending on how you manage them, but....you'll be likely wanting to AI for the dairy cow and use your dad's bulls for the beef heifers, so you've kinda got two operations going at once.

Then you're going to need to pump water to both of those spots.  So if you set up the dairy animal's little area...say along the front of your property on one side of the house, and set the water tank where it can serve both pastures, you've got less equipment....at least I've seen it done that way for smaller operations.  You could also build ONE small barn, with the shed on one side to keep the beef animals out of the bad weather, and the closed-in section on the side with the dairy animal, with the walk-in door from your yard for milking.

@cowboy might be able to chime in on this.  Don't know if he's run any dairy alongside beef or not.

I've never dealt with dairy cows so I can't help with mixing them. I assume they would need a little more feed than a beef cow.

As far as cows per acre, I'd say if you don't want to feed you're probably looking at 2 pairs max on that property. You might still need to feed in the winter, but a few bales and a protein tub would go a long ways with 2-4 head. You may want to consider fencing the property into halves or thirds so you can rotate them around and plant different grasses or legumes to keep them fed as long as possible. I don't know what your winters in TX are like. I'm in northern Arkansas and we can get >300 grazing days with planned rotations and the proper crops. That leaves us potentially feeding just the coldest two months of the year. I'd like to say you could beat those numbers in TX, depending on the weather and water.

It depends a lot on rainfall.  

If your folks raise hay, then you already know how much grass will grow and how quickly, on your land.  Up here, wtih 63" of annual rainfall or so (I think we're lower than that these days) we can keep a lot more cattle per acre than I'm guessing you can.

Like most others in this thread, I don't think you're going to get away without feeding, but it seems you have a good source for that, so you're set up well.

Good on you for letting the guy have time to find his horses a place.  

And yeah, they really graze close.  Hopefully you'll get enough rain this year to help the grass recover some.