Cush and Midian are very different places. Cush is in Africa, in the area of present day Sudan and Ethiopia, Midian is in the area of present day Jordan and Saudi Arabia. But that is not the issue to me. The issue is the Bible only ever mentions Moses having one wife - that is enough for me, but it might not be for you so I will be kind enough to share my thoughts.
The time between when Moses went to Midian and left to deliver the children of Egypt was at least 50 years. We see in the bible text that he left Egypt a young man and when he went back he was 80. Between that time what is revealed to us about him was that he was only in Midian tending the flock of Jethro. Never in Cush. My conclusion is that the Cushite woman and Zippora are one and the same person.
If she was from Midian why did they call her a Cushite? Since the text is silent I must make an inference here. Cushites were Ethiopian and very differenly complected then Israelites - they were black. This fact would make the reference to being from Ethiopia instead of being a Midianite something that would have naturally been said. Secondly, I know historically during that period and specifically in that part of the world people were very nomadic, so I further come to the second conclusion that Jethro was originally from the land of Kush and nomadically moved to Midian and settled by the mountain of God due to an encounter with the living God at this mountain and the faith he found in him.
When I read Exodus 10:29-33 you see that Moses father-in-law was promised land by God also and he told Moses to go with him, but Moses said that he had his own land that he was to take with his relatives. Moses's father-in-law new that God was protection for them as they moved on in the wilderness and asked if they could go with him for protection - so they went. Due to these verses and the fact that Miriam and Aron were Moses's brother and sister I believe this could have been a family feud. I am sure his wife Zippora (the Cushite) would have wanted to go with her father and her family and bring all the Israelites with them - then they all could be together (her possible reasoning). Miriam an Aaron began to complain about her, worried that Moses - there deliverer and leader, would possibly go with her and her family. Remember Miriam was the one that put the baby Moses in the basket to save his life, and had very recently received her brother back after so many years. If you know anything about wives and there sister in laws, this seems to me to be a very simple and natural/normal solution to this dilemma. To generalize, women are very typically sources of division and in fighting between families. I also find it telling that only Miriam was struck with leprosy not Aaron, and I think this to adds weight to my conclusion.
Furthermore, I don't believe that this was a brand new wife because since the burning bush Moses was consumed with the almighty and not these issues of marrying - not to mention he was over 80 years old at this point.
A couple more thoughts. If you look at Ex 18 and see Jethro's, the father of Zipporah's, spirituality and faith. It is obvious he believes and worships the same God of Moses. Also if you think about it for a minute Jethro was the one that lived at or near the mountain where God met Moses in the burning bush. I feel it is safe to say that it is very probable that Jethro knew in the sense of worshipping / serving Jehovah before Moses did. Secondly He - Jethro was probably the only one that ever corrected and counseled Moses in his leading of the people (Ex !8). Obviously from this text we see Jethro was like a Father to Moses in spiritual things. Because of these texts I could and would conclude that Zipporah was of the same faith as Jethro / Moses and probably preceded Moses in following Jehovah.
Another thought based on the previous texts and conclusion but also from what is known from history - the custom of that day was not to give a younger daughters hand in marriage before the older. Zipporah, being the daughter given to Moses and therefore the oldest, she would have been the one to show Moses the ropes of being a shepherd, and I would bet the things revealed to her through her father about God, especially before the burning bush experience.
Secondly, the covenant made with the children of Abraham was circumcision. We see in Ex 4:25 Moses wife circumcises there son in an act of obedience to the pre Mosaic covenant of God made through Abraham. Although it seems she complained about it.
Thirdly Moses was a sojourner in a foreign land, who else would he have married?Ex 2:21-22
Finally in the law we have to understand the "spirit" of it not the letter of it (Matt 23:23, 2Cor 3:6)which in the passage you sited was Israel going in to possess the promised land and set up an earthly government and culture. Intermarrying with other nations would have quickly corrupted the people and nation of God specifically because they served and worshipped other Gods. Therefore the law was created to protect the people and the nation. Moses's experience and situation was completely different completely (I did that for emphasis)! That is why when we talk about the law we have to understand God's purposes in establishing that rule. Furthermore the law of God always works in conjunction with what is best and applicable to the people and their specific situation. The problem isn't with the law it is holy and good (Rom 7:12), the problem is the hearts of sinful men, but that is another story for another day.
I hope this helps! Please - Give me some feed back Niclas Nilsson.