ましょうか vs. ませんか.

Hey all. So I know their meanings are similar. ましょうか = shall we, ませんか = would you like to. These are distinct enough such that I can tell their difference. However, when I see sentences prefaced by いしょうに, it becomes less clear to me what the difference is between their usage. For example, how would the following two phrases differ in their usage/translation:

いしょうに見ましょうか。
いしょうに見ませんか。

I've looked around and it seems the former phrase would be used in a context where you would expect the answer to the question to be yes. Say for example, you happen to meet a friend at a movie cinema and watching the same movie and you suggest to watch it together. The likely answer would be yes. In the latter case though, my understanding is that its making a suggestion where the response is uncertain, such as asking someone out on a date.

Or I could be completely off base with all of this. Any help is appreciated

"Together" is いっしょに, not いしょうに.

Your understanding about ましょうか and ませんか is incomplete. The agent of ましょうか is the speaker "I" or the speaker and addressee "we", so it expresses offer to do something for the addressee "shall I~?" or invitation "Shall we?/Let's". On the other hand, the agent of ませんか is the addressee "you" or "we", so it's suggestion for the addressee to do "How about~? (as the meaning "you'd better do")" or invitation "Shall we?/Let's". Thus, いっしょに～ましょうか and いっしょに～ませんか are almost the same in meaning. The nuance could change depending on the context including intonation, though.