Cross-domain HTTPS form submissions without any browser alerts

We have an interesting predicament.

We have a domain https://securedomain.com [1], inside which sits a form
that needs to submit to https://subdomain.evenmoresecuredomain.com [2].

Note that both domains are secure, but the certificates are currently separate between these two domains.

When we submit the form with the browser pointed to securedomain.com, the browsers shows an ugly alert pointing out the different certificates.

Question: is there a way to avoid this, and do this securely?

Could we have the form in [2] appear inside a "modal window" in the page [1]? I doubt this will be a solution given that the modal is an HREF for a DIV or an iFRAME but we can try.

Alternatively, can we add subdomain.evenmoresecuredomain.com to the list of domains covered by the SSL certificate of the first domain (our main domain). Will that solve this issue?

Many thanks for any pointers!