There are a few nuanced things here.
1. Is it up to you to make the decision for the group?
You're trying to prevent others from inviting Alice if they want to; based on your own personal desire to keep the group small.
This is cause for friction between you and your friends, regardless of Alice.
You mention that you're now hosting, and are therefore inclined to not invite Alice, but there is a massive difference between a hosted party, and a recurring meetup of friends that takes place in each other's home. The difference is that in the second case, the participants generally don't defer to a host, but rather choose to meet up as equals (in terms of event planning).
Are your friends deferring to you because you are the host? Do you defer to them when they are the host?
I think this is the first thing you need to address. There's no objective answer, it very much depends on your friend circle, and possibly your local culture.
If you are not assumed to be in charge of the party (as the host), then you don't get to tell your friends to not invite Alice. They can invite her if they want to (an IPS approach suggests that the friend would ask everyone else first, but this may be skipped due to Alice's earlier invitations).
If you are assumed to be in charge of the party (as the host), then you are free to not invite Alice (though your friends may disagree with your decision). Your friends should also check in with you before extending an invitation with Alice. In the end, you have the final say; but remember that the others may dislike your decision and you can't control their reaction to it.
2. Is Alice a friend? Or was she always a +1?
This makes a huge difference. In most friend circles, partners of friends are generally invited by default; but their invitation hinges on being the partner of a friend. This means that when they break up with the friend, that they are no longer included.
However, it's perfectly possible that Alice started off as a +1, but grew closer to your friends and is now deemed a full-fledged member of your circle of friends.
Several of my close friends started off as a +1, and it'd be horribly rude for me to always consider them "inferior" to a "true" friend. At some point, they migrate from a +1 to a direct friend.
I can't answer this for you. If others in your friend circle consider Alice a direct friend, then they may not like you excluding Alice.
If, however, your friend circle unanimously considers Alice as a +1, then people should generally agree that Alice is not required at the party.
3. Is there precedent in your friend circle about inviting others?
Is it allowed? Is it frowned upon? This is specific to your group of friends.
As an example, one couple in my circle of friends (who generally host the party) have no issues with us inviting others (within reason), but do object if they are expecting to eat dinner with us (because that changes the food planning).
Everyone in our friend circle agrees with that rule. If there is an impact on the food prep, the host gets to make the call. If there is no impact on food prep (e.g. someone who makes a brief appearance but doesn't stay), then they're always welcome.
You need to answer this, I can't answer it for you. But if your friend circle has established precedent for inviting others; then you'll generally be expected to follow the precedent.
To summarize
Here's the order of operations, as I see it:
If you are the host, and in charge of the party, then it's your call. However, with great power comes great responsibility: if you push to exclude Alice while others would like her to be present, that can end up causing friction between you and your friends. Exercise your prerogative as the host with caution. As the host, I would still generally defer to the group, and not try to make the decision for them.
If you are not the host, then it's not up to you to make a group decision. The group should decide. Talk to them, see what they're thinking. Try to bring up the topic without immediately stating your intention to exclude her. Gauge your friends' reaction first. That way, you prevent coming across as a negative influence on what is supposed to be a positive social experience. If the group is hesitant and not clearly leaning one way or the other, you can offer your doubts about adding another person onto the multi-day party. You'll only really get pushback if anyone has concrete objections (i.e. they really want Alice to be present). At that point, you have to respond based on that friend's objections; I can't answer that for you.
If the group decides to invite her, so be it. The group has spoken.
If the group decides to not invite her; then anyone who afterwards decides they want to invite Alice anyway will have to get the group's consent. As a bonus, this takes the leg work out of your hands, assuming that the group has e.g. a group chat and doesn't just use you as their communication channel.
If the group decides to invite her, you still have the option of flat out refusing to let Alice in your house. However, this is not an IPS approach, and it will likely damage your friendships much more than when you had simply allowed Alice to join the party. If you push this, I'm expecting a pyrrhic victory.
