He can see her for coffee first time and hear her out.  No reason to jump in first thing, step back and let him experience her.  She has not earned a jolly greeting from you.   
 

google authentic apology and look for those behaviors.  

No reason for her to come to your house. He can meet her away from the house and see what her attitude is like.

He can meet her in town. Coffee. Lunch. She has no right to be in your home at this point. 
 

stand strong. 

conversation starters for just this very purpose. My SDiablas28&26 leave for months or weeks at a time but they allllllways come baaaaack ... with their same snotty attitudes and drama. I have to figure out how to have a very shallow, disengaged greeting/conversation with them. It's weird but weird is the reality when we're dealing with toxic, phony people.

“Greeting: Hello. (Nothing more)

“How’s life?”
"Hi, I hope you had a pleasant flight/trip? You did? That's great. Well, I have <insert places to be or things to do> that I need to get to, so I'll see you later."
Response: Sorry, I have things to do. You will have to ask your dad. (Nothing more)
If she asks about anything personal:  I'm not comfortable sharing personal information with anyone who does not invest in sharing theirs. (Nothing more. Stay on message.)”

Medium Chill Conversation starters:

“What have you been up to lately?”
“What are some of the things you are looking forward to doing?” 

“What do you wish you knew more about?”
“What do you like to do?”
“Do you have any plans for the weekend/holidays/summer?”

If it requires distance, leave. Under communicating is far better than over communicating.
Just stay polite and civil and noncommittal.

I agree that he can have the visit with SD happen elsewhere but since you asked for greetings, I am answering your question.

If you want a relationship with SD or not.  SD is only coming because she needs something .  Something BM can't afford, SO be careful.  SD has any brains she would lead up to it,  like 3 or 4 visits before the  $ request 

Well, I would hope that she just wouldn't show up out of the blue with no notice.  I mean, even if she were to be local, her dad (and you) could be out. Make sure your DH lets you know about her plans.

Her history sounds difficult.  She has alternately been aligned with your home.. and with her mom's... but when at mom's she didn't make contact (not allowed? loyalty bind to not contact?) Was there any reason other than just "wanting to regain her relationship) with her mother that she wanted to make the move?  Were there underlying issues with mom.. addiction or some other issue that made her be absent for so long.

They do say absence makes the heart grow fonder.. possibly the absence of mom in those formative years left her yearning for that relationship... then mom made keeping one with her dad difficult. 

I also agree with others that you should be wary of her motives to reconnect.  They often do come with requests for help.. that of course a bio parent wants to fulfill to not risk losing that new connection.  This should be discussed with your DH.. are you even in a financial postion where you would have anything to give as a household?

As far as how to act.. what to say.

The advice on medium chill is good.  Say hello, express mild/surface interest.. but don't go overboard hugging.. teary eyed.. and certainly don't try to bring up her mom and anything like that.  Basically just surface.. let your DH figure out what she is up to.. and take it from there.  

It might be good for them to meet in some neutral location.. just the two of them first... they can say things that they may not be as inclined to with you there.. things they may need to get out.

I would also not let DH go alone.  I would be together at each other's side.

Then she can either behave reasonably and with contrition, or....  buh-bye.

When someone has told and showed you who they are, believe them.  No get out of jail free card for these types.  They have to do the work or they get no quarter.

Receive them cautiously and refer to them only by their formal first name.  Or better yet, by their first and middle names.   That sets the done very effectively.  That sends the message that their stench has been experienced before, recognized, and that you are poised to come down on them instantly if they twitch out of line.  Be present, be overtly observant, make sure she understands that she is on a short leash and under the intense hairy eyeball for any bullshit.  All communicated by body language and tone of voice.

IMHO of course.

She shows up unexpected- DH is there he answers teh door and escorts her to the car to go out somewhere for a soda pop. DH is not there and shows up unexpected? Hide and don't answer the door. :) 

First time should not be in your home. But a restaurant,   In the public where SD has to behave.  Since SD didn't come out asking for $. It's will a carful Conversation where she will drop something. College/ car/ wedding/ wanting to move out. As a starter. Hopping you will first offer money. '''I will buy you a car''' 'pay for your wedding ''  then if that doesn't work on visit two we get the ask 

As someone whose SD decided to "reconcile" after 7 years of no contact (with me), I'd prepare myself for this to be about ulterior motives (my SD was planning to get married, we later learned, and of course wanted her father to contribute--he did, but not nearly at the level she and her mother expected). I also agree with others who suggest a meeting outside of your home,perhaps first just with your DH. Get a feel for what's really going on. We were treated like crap after being open to a "renewed" relationship with SD. It wasn't worth it.