The only thing wrong with the second one is the addition of the word "to". Either one is fine. I agree that "shouldn't" would be more comfortable in the first case but is not necessary. (Just as in that sentence: I could have written isn't but, for me, spelling it out give it more emphasis.) We shouldn't eat so much pizza. We also shouldn't eat so much cake. We shouldn't eat so much pizza. We also should not eat so much cake. We shouldn't eat so much pizza. We should also not eat so much cake.

We also should not ... Better is: We also shouldn´t ... does/doesn´t should/shouldn´t do/don´t must/mustn´t But, you can write it so. does/does not should/should not do/do not must/must not