I know a few people that make the holy trifecta of small children, full time job and horses work for them, but they all have lots of money (to spend on full time childcare and horse-care!) and/or extremely supportive partners and family that are willing to do a lot of help with the children or the horse. Also a reasonably laid back attitude and ability to multi-task seems to help, as does having home/work/horse all located close to one another (if you threw in even an average length commute to work or the yard into the mix it would start to look very challenging!).
To be honest, having horses is always a total financial, emotional and time drain whatever else you have going on in your life, but also always a total joy, so if you really want the horse enough you make it work and sacrifice elsewhere as needed (you can probably forget fancy long haul holidays for example).
But there is no shame whatsoever in sticking to lessons, riding holidays or a share whilst the children are very small and build up to one of your own when they are a bit more self-sufficient. One tip to try is: for a few months put your 'horse budget' (so what you'd spend on livery, feed, farrier, lessons, insurance, plus a 5-10% margin of error/emergency fund) into a separate account and don't touch it. How does it feel financially, if you find things like kids shoes and activities start to feel like a stretch then maybe that's a sign it's not the time. On the other hand if it is relatively financially easy then that's a good sign, as you can afford to buy in extra help with either horse or DC if you need it...