What an interesting question! She would have probably have been lonely; Hamlet's descriptions of her seem to paint her as a woman who like to be in company, liked to have someone around. So, she would have been lonely. She also would probably have been a lot more stressed; many more responsibilities of the kingdom would have fallen on her shoulders, and it would have been quite a strain. She also would have had a better relationship with Hamlet, and possibly had the opportunity to oversee his wedding to Ophelia. It is because of Hamlet's fury at his mother for marrying Claudius that he alienates himself from her, lectures her about fidelity, and is caustic and rude to her. Because of her seeming infidelity, Hamlet also rejects Ophelia, who, by all counts, he had been very honorably courting, with serious and good intentions. But, because he was so angry with women, so betrayed by them, and found them so lacking in trust, loyalty and prudence, he rejected Ophelia outright. Who knows what might have happened between them if that anger hadn't been there; so, Gertrude might have become a happy mother-in-law to Ophelia. So, there would have been loneliness and stress, but balanced by a good relationship with her son, and happy times connected to that.
I disagree. Hamlet is next in line to the throne. By some means, Claudius has taken hold, but this only adds to the corruption which permeats the story because, as crown prince, HE should have succeeded the throne the minute his father died. Gertrude would not be lonely, and indeed, if Claudius loved Gertrude that much would he kill her? (Who knows, I suppose, if he killed his brother?) Gertrude enjoys the company of her son, correct? If Hamlet had been obliged to return from Wittenburg to take up his position as King, she would not be lonely.
You could say Hamlet is too young to take the throne, but this isn't true (and certainly we never really know the true age of Hamlet anyway) as we see how his depth of thought and knowledge shows he is deeply intelligent.
Her life would have probably been shorter than it actually was. If Claudius killed King Hamlet, he could have just as easily had Gertrude killed. I could be wrong, but it's entirely possible. Think about it: Claudius, because he was the brother of the king, would have become king either way. Gertrude would have possibly been kicked out the day after the funeral.