The Family That I Am A Nanny For Does Not Want To Pay Me Overtime After Working 46.5 Hours For Them This Week.

(Note: NF= Nanny Family, NK= Nanny Kid, MB= Mom Boss, DB=Dad Boss)
I normally work 32 hours a week for my main NF (NF1). 14 of those hours are done as part of a nannyshare with their friend’s child who gets dropped at their home two days a week (NF2). The remaining 18 hours are me working privately for NF1. NF1 pays me on the books. This past week I worked a total of 46.5 hours for NF1 because I did a couple date night shifts for them and MB1 was 30 minutes late coming home one day. I know that at any other hourly job I would automatically get overtime once I hit over 40 hours a week.
NF2 used to pay me on the books, and my direct deposit would come out of MB2’s bank account. However MB2 has been unemployed for a little over a year now and asked me a few months ago if they could switch to having DB2 Venmo me each week for the 14 hours that NK2 is with me each week because “money is tight.” I said yes because I did not really feel I had a choice to say no and I didn’t want them to stop bringing NK2 to nannyshare as I can’t afford to lose the income.
MB1 is who handles my payroll for NF1. She is from Europe and maybe this was an ignorant thought of mine but I wondered if she was maybe not aware of American overtime laws. I decided to mention something before leaving yesterday about how I was happy I’d hit overtime this week, just to put it on her radar. She got very irritated immediately and said they don’t owe me overtime because 14 of the hours I cared for NK1 were not private but part of the nannyshare and that NF2 pays me under the table so “why am I allowing them to break laws but insisting NF1 follow all of them” I was kind of taken aback and said that I didn’t really feel like I could insist that I remain on payroll with NF2 and that I couldn’t afford to lose the income so I rolled with it, but that I work over double the hours for NF1 than I do NF2 and I hit overtime because of the date night shifts where I was working privately for them. MB1 just glared at me and said “Okay.” It was so tense and awkward I just left.
I really don’t see how those factors impact whether or not I’m entitled to overtime. Am I missing something here, are they legally obligated to pay me overtime? Should I insist on this and what should I do if they don’t listen and refuse to pay it or fire me over this disagreement? I am very lost on how to navigate this. I am in Michigan
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