Hm. If Theodore were Tatiana's twin he would only be 17 (just) on the outbreak of war. If Olga's twin he would be rising 19. I think, and this is a personal view, that it would be difficult for him to gain much credibility with the people in wartime unless he spends time at the front.
I agree with earlier comments that it would make better historical sense to give one of the other Grand Dukes a fictitious son, who could realistically be in his thirties or early forties, with a good deal of experience of life. If you were to give Grand Duke Alexei Alexandrovich a brief 'equal' marriage about 1875-80 (he was born in 1850 and his illegitimate son Alexei Belevsky-Zhukovsky in 1871), he could then have a legitimate son who was a Grand Duke, served with distinction in the Russo-Japanese War and been a divisional commander in WW1. In between, he has travelled widely and absorbed liberal ideas. His mother could be a minor German princess who died bearing him, and a grief-stricken GD Alexei then spent his time on slow ships and fast women. The fictitious Alexei Alexeievich would, of course, be next in line to the throne after the Vladimirovichi, so much closer to the throne than a fictitious son of Nikolai Nikolaievich.
Naturally, Alexandra hates Alexei Alexeievich, who is physically all her Alexei isn't!
Ann