OP, I so sympathise with what you have said here. Have been in a similar situation.
I think there are a few things to untangle here to help you feel better about yourself.
The first is that your fat is not you. You are not your excess weight. You are a person who is clearly well-loved, well-thought of and wanted. I speak as a fat person who has finally started sorting out her weight and has a long way to go with it, when I say I genuinely believe that loved ones are being caring not judgemental when they express concerns about medically dangerous weight gain. It's not easy, but we can choose to see those interventions as loving, not critical.
Also, I honestly believe you can do what you planned as well as what others are suggesting. Of course you need to start loving yourself right as you are and taking excellent care of yourself. Have a think how that manifests. For me, it was the decision to spend money on four personal training sessions a week. That's a lot of money and time but it's made me feel like I'm worth it. Getting strong and energised and toned has done more for my self esteem than accepting being borderline obese. I don;t accept it. I'm not happy with it. I don't have to be. Nor do you., What you can be happy about, proud of, self confident in is your commitment to getting back to a weight you feel great at.
Your DH needs to be on board with this. If he can afford a bike and all the kit that entails (£££) then you as a family can afford for you to start intensive training. If you tell me he's been riding a rusty old thing and you are broke, then he needs to step up with child care so you get time every day to do some serious exercise. Online, for free, I recommend Yoga by Adriene, Kettlebells by Amy (8 mins of hard sweat, and a kettlebell is only a few pounds) and lots of other body weight HIIT you tube videos. You could also get Jillian Michaels 30 Day Shred.
With food, really focus on optimum nutrition as well as portion control. Go for minimum 5 veg, 3 fruit per day, 2L water, plenty of lean protein and small amounts of complex carbs.
Load a pace app to your phone and clock 10k steps a day.
Look for ways to be active as a family. Do buggy-walks with friends during the week and go for hikes as a family with DH carrying your child on his back instead of him going for bike rides alone. Get a child carrier to attach to his bike and go on bike rides together. The extra weight and care he has to take of your DC should make his pace right for you. Make a list with him of family treats and outings that are fun and healthy - a day on a remote beach or wandering around woodlands, exploring castles with DC, building dams and dens. Get a trampoline. Do the garden together. Find ways of making life more physically active together.
Explain to him and your family that crash dieting doesn't work and you have no intention of making yourself ill, so if they want to be supportive, they need to understand it's a long, slow process. He can help by not keeping trigger foods in the house (e.g. I ask DH not to buy ready salted crisps. I can leave other flavours but plain crisps are my weakness. When I buy treats for him and DC I buy stuff I hate - biscuits I'd never eat, ice cream flavours I dislike. And keep healthy treats for you to hand - fresh berries, melon and pineapple, greek yoghurt etc. That makes it easy to stick to your healthy eating plan.
Log your calories with My Fitness Pal or similar. You'll soon find what you are prepared to spend calories on and what isn't worth the bother.
I still have really down days when I wish I'd done this ages ago and berate myself for letting my weight slide so far. But getting fit and super healthy really is a worthwhile, self-loving plan to have. And you will quickly feel better on it than any sort of crash diet or body positive attitude that at heart you have no faith in.