A priori, I see no large risk on the underlying on your trade, since the (roughly null) deltas on both trades will offset each other. The breakeven move on a straddle is $$\left|\tilde{\sigma} S \sqrt{\Delta t}\right|$$; you should just have a residual exposure on the term structure of volatility.
Suppose that at some point $$\tilde{\sigma}_\text{March} > \tilde{\sigma}_\text{April}$$. If between two delta-rebalancings, your realised volatility is between the two, you will lock in a loss on both trades: gamma loss on the April straddle and theta loss on the March straddle.