This isn't difficult unless I am misunderstanding something.
Upon Arthur Tudor's death, Henry VIII (who is not the VIII just yet) is next in line of succession. Presumably the new baby Mary is second in line.
Since Catherine's marriage with Arthur is obviously consumated, Henry VIII presumably never marries her. Instead, he marries someone else.
If Henry VIII and his new wife have any male children, those boys become next in line of succession. Mary, however, will come before any daughters Henry VIII has.
It is highly unlikely the Tudor court will allow Mary to leave the country until a male heir is born. Because she is in the succession somewhere, the Tudor court will be very protective of who marries her as that person could become Prince Consort of England, perhaps even King.
Catherine will likely not want to leave her daughter, so she will likely stay in England unless international politics force her to marry another again.
Well, legally Mary was inherited her father's position in the succession. But given her youth, I think Henry VIII would be proclaimed King as she'd just be a young girl--and thus "by passed" so to speak. As I outlined below, English succession favors the sons of the monarch, followed by daughters; any issue of sons is much the same, with boys coming first, before girls. In this case of Catherine having a daughter and Arthur still dying, the succession would technically be Mary, with Henry behind her. Being a female does not push her back because she would as her father's only surviving child, take his position in the line of succession.
The Privy Council would be quite unlikely to want a young girl as Queen Regnant or a Regency, however. So they'd certainly want to crown Henry VIII over her.
So Henry VIII would of course become King, and his issue would follow the same rule: sons before daughters, then Mary. Mary should technically be Queen in this scenario, but I just don't see it happening given her age. If she was older, possibly.