You can certainly do it on your own - we have had a nanny for years and I do all our paperwork, filing etc. on my own. Fortunately, after you’ve got everything set up, it’s not all that arduous.
From a contractor vs employee standpoint, the nanny would (by any definition I’ve read) be considered an employee.
You have to have a federal employer ID number, and a state employer ID number, and a state unemployment ID also; well, depending on your state that may vary of course. We’re in Virginia so I speak from that standpoint.
I file two quarterly “returns” for the nanny: one is her state income tax withholding (my nanny has opted to not have state tax withheld; this is legal in VA as long as it’s all reported; she sorts it out when she files her annual return). Basically I go to the state revenue department web page, log in, put ‘zero withheld’, and I’m done. The other is the quarterly unemployment. That I do have to do a little more arithmetic - only the first 8,000 is subject to unemployment tax so I have to figure out each quarter whether that’s been exceeded, and by how much. And I have to pay a few dollars in unemploymenttax each quarter (it’s never been more than 30-40 for the year). Again, this takes a couple of minutes on the state’s web page.
At the end of the year I file an end-of-year state tax return, I also have to file W-2/W-3 stuff with the Social Security Administration. That takes a little longer… though not much since I found the SSA has a web page that does the job - I plug in my numbers, they create a PDF, and I print a few copies. I give one set to the nanny, another set to the SSA, another set to the state.
And when I do our annual taxes, I have to fill out a Schedule H (think that’s it - Household Employees). I say how much I paid her. It has me calculate the social security/FICA and I remit that, plus any federal tax I’ve withheld. BUT - basically it adds to my bottom line tax bill. If my normal taxes for the year were 10,000, and the FICA/fed tax for the sitter was another 1,000, then my tax bill is 11,000 - and I need to have that covered via withholding or quarterly estimated taxes. I handle that by an increase in the amount my employer withholds - rather do that than forget to file my quarterly.
Anyway - it sounds like a lot, but after the first year, it’s fairly easy. Quicken and Excel help a lot.
In the situation you describe… I guess one approach would be to have one family do all the tax paperwork, and you just compensate them for their portion of the FICA. That might be tricky if you both have flex spending accounts, or want to deduct the childcare expenses on your federal returns. The more straightforward approach, really, would be for each of you to handle it separately.
I am NOT an accountant though I did have professional advice - my mother - when I was getting started with all this. Feel free to email me though as noted, I’m not a pro so you’ll want to double-check on the laws where you are. And if you know a tax professional, definitely consult him/her.