I wonder if what might actually help is some tips on how to manage two kids at the same time, from other MNers who have done it? Ignore me if not, but I feel like that's the source of your stress, as opposed to whatever the GPs do or don't do. When you start to feel confident managing two on your own, you will feel less resentful! It is hard, but there are things you can do.
First sort the transport - so either baby in structured carrier and 3yo in buggy, or baby in pram and 3yo on buggy board (the one with the seat is worth every penny imo!), or baby in either and 3yo on scooter/trike/balance bike etc, or walking, reins if needed. Completely depends on the individual kid but find a way that works, that the 3yo enjoys. Go for walks to feed ducks, find a Gruffalo, fairy houses etc. Sling for around the house, if baby will tolerate.
Get used to parenting from the couch! Play Simon Says or musical statues. Use Cosmic Kids Yoga, Danny Go etc on YouTube. Get an easel or magnadoodle and have 3yo draw things and you have to guess what it is.
Get 3yo as involved as possible with looking after baby. If you're weaning, this is a great thing for older children to help with. Get one of those baby food sizing things (I don't know what it's called but it's like a plastic tube, and if it fits in the tube the baby can choke) - 3yo can help with chopping food and putting it in the tube to test it, and also doing the "squish test" to make sure food is cooked soft enough.
Divide and conquer as much as you can - so when DH is not working, don't all go out as a family (I'm not saying not ever, just not for the whole day). Let DH take 3yo swimming or to the park and you look after baby, then all meet up for the afternoon. Swap over when you can (weaning will also help with this!).
Do whatever you can to spend a bit of one on one time with 3yo every day - a really focused 10 mins will help even if you have to be looking after the baby for the next hour. Stick baby in front of the dancing fruit for 10 mins if you have to!