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Since you have quite a few unsecured cards, I don't see any reason to go back to a secured card with Citibank.
If you're interested, I think you could qualify for the Dividend (5% rotating categories) or the ThankYou/ThankYou Preferred. The Diamond Preferred is a good balance transfer card which you would probably get approved for. If you are feeling more ambitious and fly on American Airlines at all, you could also look at their lower-tier AAdvantage cards.
You need to be focusing on having no inquiries at all for at least 6 months prior to the mortgage app, and your utilization needs to be as low as possible going into that.
I see no purpose for the card. Focus on stashing cash away for closing and paying down credit card debt.
Focus on getting the mortgage. The last thing in the world you want is your app held up or uprated (or the dreaded DTI denial) because you have too many inquiries or your util is too high.
Once you've closed, feel free to go nutso and apply for whatever you like. Best advice would be to pursue a Diamond Preferred with them after you've closed on the mortgage and get rid of the low limit cards altogether.