First of all, if you’re single, never married and have no kids, dating someone who’s divorcing, who will have an ex-wife to co-parent with, and visitation or joint custody of his kids, is very different than what you’re used to. Your boyfriend has a lot of commitments — in addition to regular old work! If you stay together, you’re going to have to be mature enough to understand his own needs and responsibilities as well as your own. Make sure you’re compatible (and honest with yourself about what your needs are) before you move further.
If you’re truly understanding of his other commitments, you won’t get so annoyed and act out when he’s not with you because of them. In fact, you’ll be glad that he’s taking care of his own business so that when he is with you, he can be “all there”.
That said, since you’ve already placed an ad looking for a new relationship, I think you may not be willing to wait for him or to put up with his lifestyle, which is different than yours. There’s nothing wrong with that, as long as you’re honest with yourself about what you want, and what you’re not willing to bend on.
As far as being friends and hanging out until he’s finished with his divorce and more able to be free for you, I don’t think that will work. The reason is that you’re ready to start dating again — with him or someone else. He’s going to be jealous and feel betrayed if he knows that while he’s doing his so called work with his divorce, you’re out looking for love.
The more difficult, and maybe more mature position to take is to admit that this relationship won’t work right now, but that you both love and respect one another. Let go of each other, and if and when he’s divorced and his time is more his own, he is totally free to ask you out.
I know you say you love each other, but if you’re not compatible, the love doesn’t work. You’re seeing that already.
Let me know what happens — and good luck! 🙂