Consent is an enthusiastic "Yes!" not the absence of no. I disagree with LH's notion that blowing her GRE attempt by holding her to "her word" (unclear if given) after taking this job despite her objections ("I understand, but") will lead to respect or sex. If she fails, it'll be the day she "failed the GRE because of you" and you "were told 'k' so it was her fault she failed." What will that evening of work cost in therapy? What will that do for your chances of reconciling?
I do think you'd earn respect by telling her you love her and are there for her and will ensure she won't fail her GRE due to a miscommunication or interference by baby--whether that means staying home or hiring a sitter for that $175 (so you get future jobs from that guy). I do think you'd earn respect by asking what she means by "Considering the help I get is minimal"--and how to get childcare much closer to a 50/50 shared responsibility outside your day job hours.
