I think the space you currently have is okay for part-time stuff, the occasional video, some storage etc but, given the nature of your work, I think the time will always come when you need bigger work premises. As moving house is unrealistic, then that means obtaining separate premises is inevitable. The recent happy arrival in the family is going to generate space needs of his own, his toys will need more storage space than yours, and he will have mum on his side.
That brings me to the advantage of working at home: Seeing the Sprog grow up. Thinking about it though, having separate work premises does not mean you have to be there all day, every day. Phone calls are easy to divert, and unless you are using it as some sort of shop (unlikely) then the only callers will tend to be postal / parcels delivery, which can be signed for by front desk staff (if that facility is available).
It feels that electronics is increasingly a desk job, whether it be CAD, research, reading data sheets and app notes, or performing general admin. There is no reason why that cannot be done at home (to spend some time with Junior) or away (to get some peace and quiet). That just leaves the physical aspect of electronics, which might boil down to only 1 or 2 days a week on average.
That only really leaves the financial aspect. I always feel it is more professional to meet prospective clients in a work environment rather than home. In my experience, the perception is that if you are at home then you "must" have lower overheads and can charge less. If work improves, it leaves the possibility of perhaps working alongside a business partner, or sharing costs with a similar small business in the same office. Depending on the lease, if work didn't go quite so well then you could probably walk away after 6 months. I know SWMBO wouldn't be happy about taking over the rest of the garage and leaving the Davemobile outside, but I'm afraid if that's what it takes to pay the bills, then that's that.
Which is my long-winded way of saying you don't have much to lose by at least investigating the market. Go for it!