When I'm at home I am happy to slob around in old track pants and hoody but when i go out I am varying levels of effort and always have.
My dc are teens now so I am actually conscious of not embarrassing them. If their friends / boyfriends etc are over I will not dress in my old house stuff but I will wear newer versions of similar so not so scruffy.
I work outside the home and dress for work everyday. It's in a creative sector so not corporate. I dress well and have always had an interest in style. I keep my hair done and wear light makeup and always have nice jewellery / perfume etc.
I think over all I present well and I am now in my early 50s. In fact looking back at photos I think I look better now than in my 40s
It also models self care to kids from an early age. I aways did it for me as I have always been very interested and always worked in a sector where I have a lot of freedom to experiment with my style.
dh is always complimentary too and I like that. We're together over 20 years now and we still love making an effort for each other.
My advice is - do it for yourself. It will boost you in so many ways. Buy some nice clothes that fit you properly to whatever budget you can manage. It makes no difference if you're buying from a supermarket or high end once you feel comfortable, they're clean and they fit you and most of all - they're fit for the purpose you need them for. In your case that could be wide leg jersey tousers with nice trainers, & a top. Or a dress and tights and flat boots etc
Make sure you take time for your own self care - shower / bath daily, skincare, do your hair - no need to dye it but do keep it in shape and styled and brushed etc. Unkempt hair doesn't look good on anyone.
I am sure you, like most of us, have things stashed away 'for good wear', forget about that, just start using it all. Wear that nice scarf, or perfume, or top.
Good luck op, you are in the trenches with 2 small kids and working etc but please don't lose yourself. You are a valuable person too and you also need cherishing and looking after too. This can be so easy to overlook but it really damages your self worth and confidence and you want your children to have these in abundance and that starts with you.