There are plenty of challenges there for sure. And I see from the note under your name that you are planning to walk the
Camino Frances. If you want to begin in SJPP or Roncesvalles or Pamplona - depending on how far you want to walk each day - plus travel time - I guess you are looking at 5-6 weeks away from home. That may be a big part of the logistical challenge.
If you prefer to walk your first Camino 'in one go' for want of a better description - rather than stages over a number of years - you might consider a shorter camino than the Frances. This would mean all of your arrangements to ensure your family members, business and pets are taken care of would be for a shorter timeframe. This may make your dream more achievable, sooner rather than later?
For example, the Camino Primitivo from Oviedo to Santiago de Compostela typically takes people between 12-14 days. The Portuguese Way from Porto to Santiago de Compostela is similar length. There are others but, for a first time Camino, I'd recommend one of these two may be more likely to give you the Camino experience you've been reading about - including excellent infrastructure, opportunity to meet others, and to finish your camino in Santiago de Compostela. Either of these caminos plus travel time would be achievable with 3 weeks away from home.
Also, the starting points for these are relatively straightforward to travel to - so that's time efficient. For example, for the Primitivo, you could fly into Madrid and take a fast train to Oviedo. I'm biased towards the Primitivo as it is a particular favourite of mine. It very much has a Camino feel about it - without large crowds - and the starting town of Oviedo is a gem, as is the other major town it passes through - Lugo. Also if you are not already aware, the Primitivo and the Frances join in Melide about 50 kms before Santiago.
I do hope you can work out a way to walk your first Camino before too long.
Best wishes