Mary, being a young, fairly attractive, and powerful woman who ruled three North Atlantic realms, soon attracted many suitors, which, in the eye of her royal makars, were "like Helen attracting a thousand ships." Among the suitors were Philip II and Archduke Charles, both of whom were vetoed by the English Parliament and Scottish Parliament.
Even more controversially was the issue of the Council of Trent. Mary wanted to send delegates to the Council, but Protestants, fearing Papal pressure to set up an Inquisition chamber, tried to block this. Eventually Mary sent an Irish bishop to the Council, as Ireland was much more Catholic and it would attract much less religious discontent, and promised that the proclamation would stay in force.
Since Mary’s only heir was a little girl, her upbringing became a source of controversy. Scots wanted her to be brought up as a proper Scottish princess, while the English wanted her to be brought up in England and be sent to Ludlow once she grew up. Ultimately it was decided that Princess Margaret Antoinette would be brought up mostly in England and then sent to Ludlow, but would nevertheless learn about Scottish stuff(include its culture, languages and political system) and would often visit Scotland. Regardless of those disagreements, Mary and her close associates ensured that the heiress to the throne would receive an excellent humanist education appropriate for a queen regnant.
Eventually, the Scots lords found an ideal candidate for Mary to marry: John Hamilton, son of the very Earl of Arran bastardized by the Franco-Spanish peace treaty. By marrying him, Mary would be able to reconcile with those people, both English and Scots, who felt alienated by the Franco-Spanish peace treaty.
Matthew Stewart was angry, but since Charles Stewart was too young and Lord Darnley was already married to Katherine Grey, he had no alternative but to accept this, especially after Mary appointed him as a member of Privy Council of Scotland and re-assure that the Hamiltons of Arran would not be re-legitimized for the sake of throne of Scotland. Mary, after serious consideration, accepted the proposal. Together with John Hamilton, now King-Consort of Scotland(but without political powers), Mary had two other daughters, Elizabeth and Catherine(named after Elizabeth of York and Catherine de Medici, respectively).
Things went fine for a time, until a Habsburg plot was discovered: Philip II planned to orchestrate a coup by the Earl of Huntly against the moderate government, install him as Lord Lieutenant of Scotland and then push forward for a full inquisition in the British-Irish Isles. The plot was thwarted and the Earl of Huntly was destroyed(somehow later than OTL). In response, Philip II sent an armada against Mary with the explicit goal of regime change(22 years earlier than the OTL Armada), but in spite of its seemed advantage, the armada was defeated by the Scots-English army.
Mary continued her personal rule, with England going mostly peaceful, order mostly restored in Scotland, tensions between English and Gaels in Ireland subsided somehow and royal succession secured with three princesses. As she reached the majority, however, rumours about a Henry VIII-style great purge started circulating in Scotland as Matthew Stewart and other Lords knew that Mary could reverse all of those grants and attainders made under her minority, although in England things were largely quiet aside from a few grumbling Puritans writing some controversial books, at least until a scandal broke out.
Mary Hamilton, a scion of Hamiltons of Arran who served under Mary as a maid-in-waiting(following the Hamilton marriage), was found to commit adultery with Lord Darnley(who, being a senior royal, was frequently seen in court). She was soon imprisoned for adultery, but rumours about Mary’s court being a court of Jezebel soon arose among Protestants, and a ballad somehow spreaded among Scots, which somehow conflated Mary Hamilton with the Four Maries, the core ladies-in-waiting for Queen Mary. Unlike in OTL, however, since all of the heirs to the throne were religiously fluid lasses and John Hamilton was fairly popular among both Scots and English, attempts to depose Mary had been unsuccessful. As time passed following the scandal, Mary gradually regained her popularity, and Princess Margaret Antoinette was greeted with massive welcome when she was sent to Ludlow as heir to the throne. By the end of Mary’s reign, peace had returned to the British-Irish Isles, and the prophecy of a new Deborah had indeed came true for the people of the three realms.