I have to say I didn't see it as Sansa having a deliberate plan for the battle or hiding the knowledge of the Vale forces from Jon because she didn't think he could handle it or not give them away or anything like that. After what happened with the Boltons she know longer trusted Littlefinger, and I think no longer wanted to be dependent on him. That's why she said she didn't want his help, and she didn't tell Jon or anyone else about the offer since she didn't want that decision taken out of her hands. However, after they have gone to all the Northern houses they can and not got the support they need, and when it's clear that Brienne won't be coming back with the Tullys (or at least on time for the battle), she realises she has no choice but to go back to Littlefinger. As for why she didn't tell Jon about it between writing the letter to Littlefinger and the day of the battle, it could have been due to guilt about not revealing it sooner, it could have been because she didn't yet know whether Littlefinger was even going to show up... or it could have been part of a deliberate, elaborate strategy to let Jon lose all his forces but ensure that Ramsay's forces were caught unawares. Personally I think that third option is by far the least likely, and doesn't really fit with what she was trying to tell Jon Snow before the battle (don't attack Winterfell yet, wait for more numbers from "somewhere", don't let Ramsay provoke you into attacking first). Also it doesn't really fit with her motivation shown earlier in the season, which was clearly wanting to win and reclaim the North without being beholden to Littlefinger - deliberately intending for Jon Snow's forces to be decimated and Littlefinger's to remain mostly unscathed achieves the opposite, giving Littlefinger more power.
I think that Sansa didn't fully trust Jon Snow enough to inform him of everything, and I think she gave up on Rickon because she knew that it was a lost cause if Ramsay had him and that holding out hope would allow Ramsay to manipulate them (as he clearly did). But I don't buy that she was some cool calculating strategist who intended the battle to play out the way it did - she just knew that Ramsay was extremely dangerous (although she didn't really have any good ideas on how to outsmart him) and she knew that her secret trump card of Littlefinger may be coming to help, even though she really did not want to ask him for help.