There are a couple of things that you really need to tease out before you can figure out if it will work for you and your family to RE alone.
1. Do you have joint or separate finances with your husband at the moment?Whatever you have, expect to continue it in RE. This may raise the question of whether or not you can really FIRE alone, or whether you will in fact be a SAHW (stay-at-home-wife - i.e. keeping the parenting part out but acknowledging that you are being financially supported by your husband). If you have joint finances but are not in a position to theoretically both RE together (whether or not your husband wants to) then you are not REing, you are becoming a SAHW and I think you ought to take on the bulk of the household load in order to acknowledge this. If you have separate finances, then you need to decide together whether things like paying for childcare or a cleaner are a joint expense because the kids and house belong to both of you, or an expense just for you to take on because otherwise you would be doing them.
2. Do you enjoy spending a lot of time with (your) small children?People like different phases of their children differently. I could take or leave a baby, but I am loving having a toddler. He's like my little tagalong buddy for everything I want to do. Assuming your children go to school at a normal age, do you actually like spending alllllll day with your babies, toddlers, preschoolers? You say you don't want to be a SAHP, but it seems like it's the housework stuff that you're concerned about most, not the parenting. However, unless you pay for childcare (see #1 about whether or not you can afford it) then you will be spending all of your waking hours (except naptimes, I <3 naptimes) with small children. They will learn to play independently, but not for A While and if you want to have more, then think about how many years that is until they are all in school. However, don't look at the bill for full time childcare and think you can't afford any. Two days a week, or just mornings, or just a mother's helper... there are a myriad of options that will fit whatever you want to budget for part-time childcare. This post (part of a series) is specifically about mothers helpers, but I think it's a really helpful way of framing how to organise and pay for part-time flexible childcare:
https://amotherfarfromhome.com/pay-mothers-helper/3. What do chores and parenting look like now in your household?Are they equal just because you're both working? If not, or especially if you're not sure, you might want to check this out:
http://equallysharedparenting.com/ Do you and your husband both agree about what chores need to be done and how often? Do you both agree that small children are a lot of work?
You say you're concerned about losing bargaining power. One way I have heard of for splitting chores is to ensure that you both have the same amount of free time. If you did retire to read novels all day, what would be your reasoning behind being able to have so much more free time than him? Have you saved up your stash separately or together? Have you both contributed equally to household expenses? How much has your husband contributed to your being able to RE?
4. What kind of "structure" do you imagine you need? What would you be procrastinating? What would your husband be micromanaging?Is this just about cleaning? Because that's actually a very easily-solved problem. It has three steps:
i. Agree on what jobs need to be done and how often. This is about little-picture things like laundry and big-picture things like painting the house. A good way to do this is to write down your lists separately and then come together to compare. This includes what standard things are to be done to. Turns out my version of "the countertops are clean" =/= Mr SLTD's version. THAT came as a surprise!
ii. Agree who is in charge of which job. We have the "Captain X" system in our house. For example, I am Captain Laundry and he is Captain Dishes. It doesn't mean that I physically do 100% of the laundry or he physically does 100% of the dishes, but I am responsible for keeping mentally on top of laundry and doing what it takes (including asking him to put a load on or whatever if necessary) to ensure everyone has clean clothes. I have recently taken to unloading the dishwasher in the morning with ToddlerSLTD because he loves it, but it's still Mr SLTD's job to check it's been done and I have no obligation to either do it or not do it, or even to remember to mention if I've done it or not, because mentally it's his chore. Similarly, I am Captain Meal Plan and he is Captain Go To The Shops You could split it any way you want - by chore, by day of the week, whatever. You just have to both agree.
iii. Agree on how to give feedback to each other. You know who is in charge of completing a chore and you know what "complete" means and you both agree. Now it's time to agree on how you will draw it to the other one's attention if you are not keeping up your end of the bargain. Weekly family meeting?
And optional fourth step: hire a cleaner. Cheaper than divorce!
5. How's your marriage generally?You said you argued constantly while you were furloughed. Admittedly this is a stressful time generally, but that doesn't sound very pleasant. Much like having a baby won't save your relationship, it sounds like you REing might bring out qualities in your marriage which are there are the moment. Presumably for good or for bad, but I'd be careful about wanting to work on your marriage before REing if it's likely to be contentious. If your spouse were totally on board it would be a different matter, but you'll need to be communicating extra well as you figure out the "new normal" for your RE life.
6. How's your parenting generally?Obviously you just have a baby, but I'd be interested in how you both view parenting - is it work or fun? It changes in nature as your children grow, but I'd make sure that both of you have experience of doing a full day with the kid(s) 100% alone before you RE. You can check if you're cut out to SAHP, and he can check if it's a vacation to full-time parent.
6. Could you go part time?If you want structure and extra money to pay for household services/childcare, could you go part time? Best of both worlds!
If I were you, I would plan to work until your children were in school and then RE. School is free childcare, so no worries there. You'd be around to pick them up and help them with homework, and so not need to pay for any holiday or after school care either. School gives structure to your day, week and year. I would use some of the extra stash to hire a cleaner and just commit to keeping on top of dishes and laundry yourself.
(Note: if you feel you are a slob, PLEASE check out Dana White's book "How to Manage Your Home Without Losing Your Mind". It's been life-changing for me. She TOTALLY gets that most books about cleaning are written by...clean people who actually have no problems cleaning.)
WRT the structure SAHP thing... I have to say, right now that is NOT a problem for me. Nothing gives structure to your day like a toddler who passionately loves routine. And there is no alarm clock as good as a baby! When my parents looked after ToddlerSLTD when I was giving birth to BabySLTD, I wrote out what we usually do in a day and holy crap there is so much routine stuff that we do every single day. 7am get up, drink milk, have breakfast, do dishwasher, hang laundry, play or go to playground or playgroup (not now!), get home, have banana, have nap, have lunch, play, snack, play, tidy up, dinner, sweep, bath, prayers, story, bed...and that's just the Sparknotes version. I also hate cleaning but have made a couple of things part of his routine so now HE reminds ME to do them! And it's much more fun to do them with my enthusiastic little buddy who wants me to sing songs about dishwashers.
I have a friend locally with a two year old and she does a free or low-cost (like £2 church hall playgroup) activity every day Mon-Fri, plus playdates. I would go nuts doing more than two things a week max. If you fundamentally like spending time with your young children, SAHP is what you make it. Want to do loads of activities? Do! Want to chill at home? Do!
Sparknotes of this post, then:
1. Are you truly FIRE by yourself or do you just want to quit your job?
2. How can you stop arguing about chores, whether you RE or not?
3. Do you want to spend all day with your small children or not? If not, can you afford childcare, and how will school change your plans?