B.,
Take this as you will, but I would hold off on having him move in. Urgency is not a good way to begin a live-in relationship. Even if you are not a Christian and don't see this as sin, there are signs here that should trigger something. It "not going over well" at even the suggestion of him taking a medicine should give you at least a yellow flag, if not red, that he may not be willing to consider anyone's situation than his own.
Also, think about your own plans. You say that you'd like to own the business that you currently manage. Wouldn't it be easier on you to keep things as they are and continue to date your boyfriend, rather than have him move in, and work around the bumps of two people who have just moved in together? What if things don't work out or there are things you discover about him you just can't live with? Then you have to pile that stress on top of work stress and your hopes and dreams of owning the business may go down the tubes.
And your dogs - obviously you love them or you wouldn't have 6 of them! To replace 6 of them with one man, and to try and find a home for 6 animals in today's economy - people are dropping their dogs and cats off at the shelter left and right because they have to choose between their dogs and feeding their children. This is not the case for you - you love them and what would they do if their mom just abandoned them - all 6 of them. I don't know how your animals are, but I only have two dogs and one of them won't even eat when we go out of town, even though they stay with family! As soon as we come home, they cannot WAIT to snuggle with us and play with us.
And lastly, your kids. What are you teaching them about a relationship of their own - please don't misunderstand me - I'm not chastising. But when I make decisions - huge ones, especially, I always consider what it says to them. And what this says to them, is you are willing to give up your animals and their animals, have a boyfriend move in with you, who by the way is not even willing to TRY and meet you halfway or compromise, and that urgency takes precedence over making sure your decision is the right one, not just the convenient answer.
Please reconsider. True love waits, period dot. If you're worth it to him, he'll not only wait until you are ready and not rushed, but true love ALSO meets halfway. Make sure he is really the one (and that maybe his being allergic is not divine intervention) before you make a HUGE step in your life and affect the lives of your children and your 6 pets.
P.S. B., I hate to add this as an afterthought but also consider what it will be like for your teenagers. If he does not have the same schedule that you do, your children, your teenager daughter will be home alone with your boyfriend. You might think you know him, but what if the unthinkable happens? Whom do you trust with the truth? Him, who you just met, or your daughter? I'm sure with an 18 yr old and a 16 yr old, they each have different schedules so even saying your son would be there when she is there may not always be the case. Please please reconsider and give it a lot more thought, regardless of when the urgent move-in date is.