Maternity Leave

Go back a step, I don't think this is a terribly practical idea because US LPRs must have their tax home in the US and clearly if you're married to a US citizen who lives there as well your tax home would be the US under any reasonable determination. If you carry on working in Canada then maintaining LPR status in the US will be quite hard because of the physical presence test required to maintain it. A claim of permanent residence is exactly that.

You can claim a foreign tax credit on Form 1116 but you would effectively be paying Canadian income taxes once you'd paid US tax on your income and claimed the foreign tax credit. You'd have to file a non-resident TD-1 with your employer and as you're not actually a resident you lose stuff that residents are eligible for.

For example: OHIP eligibility - "you making your primary place of residence in Ontario", which it wouldn't be.

For EI maternity benefits, there are various (pretty old) agreements between the US and Canada concerning EI which basically boils down to the fact you claim where you live (with a wide variety of caveats), and as the US has no equivalent you would receive no benefits (unless the State provides them). This is a bit more of a tricky one though, I'd look it into it further there may be conditions under which you are eligible because you're still working in Canada and paying EI withholding. There was a big thread about EI on here, look for it.

Basically, Canada likes to deny benefits to anyone if there's a hint that they're not resident, but conversely, the CRA likes to tax anyone if there's a hint that they're resident.