Disclaimer: everything here has LMoP spoilers. I don't intend to mark them as such, since it's a very LMoP-specific question, and anyone reading the answers should (probably) be a DM running it anyway.
Reaction against the party
It is implied she's fine with that.
In the Joining the Zhentarim section for Halia, it says
Even if the party wipes out the Redbrand gang, Halia might still extend the offer in an effort to gain friends (and spies) within the party.
So, for me, it implies she is at least fine with that, if there is a character that draws her attention, she will invite them anyway. This means she probably holds no grudge on the party.
Also, the book only mentions
100 gp to eliminate the Redbrand leader, [...], and bring her any correspondence found in the leader's quarter.
Nowhere in the quest she mentions she wants the Redbrands alive - nor it's stated in the book as a caveat for DM-only to know. Again, that implies it's fine.
Her domination plan
The thing is: LMoP is a short adventure. In-game time, it takes a few days/weeks, depending on how your players/PCs are acting. That is one of the main reasons most of the faction plans, alliances and details are not presented - by playing only LMoP, there is not enough time to actually see any of them happening. An explicit example of that intent is
Wheter Iarno stands trial for his crimes is beyond the scope of this adventure.
Other than that, it is up to you and how you intend to keep the campaign going. If you are going to end it as soon as LMoP ends, I would not worry about it too much. There isn't much interaction between the party and the Zhentarim or with Halia left.
Otherwise, if you are going to follow up with another published adventure (preferably one that is set in the Forgotten Realm, which good for you - almost all of them are), check what the Zhentarim are doing in that adventure. Without knowing how you will follow up, it's hard to tell you anything.
Personally, I'm currently running LMoP for a few new players and they are very... murderous. They didn't get to Glasstaff yet, but they should in the next session - and it's very likely that they will be killing everything in the way. They keep one prisioner to get info and kill everything else. And the prisioner is usually mutilated during the combat where he was incapacitated. Glasstaff will probably survive though, since he explicitly asks for mercy and the party is very friendly with Sildar. The adventure takes place inside a homebrew campaign that will contain many published adventures along some homebrew factions from me. I hope this doesn't make it a Bad Subjective answer, as I haven't used my own solution yet. I believe I have enough experience in DM'ing and that experience is translated here, even if this particular solution wasn't tried out yet.
This is how I'm planning to run it:
- Halia is going to reward them anyway, as long as the PCs deliver the correspondence as well. I disagree with Hamstertron interpretation that Halia wants Glasstaff dead - she wants him out of his leader position (that's how I read "eliminating" him). As long as he can't come back, it's fine, which means being sent to Neverwinter is a solid solution for her.
- She will stay in the city, keeping to grow influence and creating a spy network around.
- If the party succeeds in the adventure, Phandalin will actually be their stronghold from now on - Halia's network of spies will either be powerful allies for them or the biggest problem in running the city. That depends on later interactions with the party that are not described in LMoP.
I don't intend to make her have any interactions with the Black Spider simply because the Drow should die in the end of the adventure, so she overthrowing him is awkward, and allying with him would make her an enemy for the party, which I don't want to make so soon. Rather, when the Lost Mine is recovered, she also has plans for that.