If you have Presta valves and don't have a valve cap on, then if the tip loosens a bit (or the brass nut which seats them to the rim comes loose) then you can easily lose air or damage them. Schrader ones ought to be fine, unless you've hauled on them with a very heavy chain and they've somehow developed a tiny hole. It's not that easy to do to be honest so maybe there's a small unrepaired hole somewhere. Just take the inner tube out.
Put some old clothes on (!). Get the wheel off as you did and release all the air. Compress on the tyre whilst pressing on the valve pin (schrader) or after unscrewing the top to loosen (Presta).
Pop 1 - 3 tyre levers (or the back of a spoon if you have none) under the rim about 3-4 inches apart so that the hooked end of the tyre lever can be held by slotting horizontally into a spoke. If you use 3 then by the time the third one hooks a spoke, the first will then likely fall out. Once the tyre starts coming free of the rim on one side, pop your fingers under it and run them round the rim. The tyre will slide clear of the rim.
Then turn the tyre so the valve is uppermost and push it up through the hole. Slide your fingers of the other hand in under the tyre, pull the valve up clear of the rim and just carefully tug the inner tube out. The tyre will still be on.
Then just fit another tube. It's dead easy - push it under the tyre so the valve slides in through the hole and feed the tube in under the tyre so it sits roughly in place. Then get your pump and pump a SMALL amount of air in so it just holds its shape.
Then all you need to do is push the side of the tyre you freed back onto the rim. Go round it until you get to the last bit. Then if it's tight put the wheel flat on the floor with the bit you've got left to re-seat furthest from you. Pop your knee on the middle somewhere (easy with a hub motor !). Grab the tyre from the back with fingers of both hands and use your thumbs to push AWAY from you against the rim. You can get almost any stubborn tyre back on this way but most are easy.
Likely won't take you more than 15-20mins even very 1st time unless you have an extremely tight tyre.
I reckon I could get the back wheel off easily. I've tried working on it before but had great difficulty aligning the wheel and doing the nuts up afterwards.
Do you have a derailleur ? Sounds like you may have horizontal dropouts like I have on my Agattu ? They slope downwards when the bike is upside down rather than the vertical dropouts which are cups you just drop the wheel back into. Horizontal dropouts are a b'stard at times. Trouble is that if there are wide slot dropouts and washers over the axle which have a lip that sits in the open end of the dropout (and help hold the wheel in the correct position), the washer threads wear they may need replacing. Otherwise your wheel will slip every time you try to tighten the nuts so you can never seem to get it to stay where you want it ... and when you do get it in it slips after a few miles.
The best way I found to seat the wheel is to loosely tighten the 'chain' side axle nuts until it's roughly where you want it. Then do the same on the other. If the wheel slips away from you when you're tightening up then you have a washer problem. Try to centralise the wheel in the dropouts - ignore any mudguard and the brakes. You can adjust the brakes later when the wheel is correctly seated (rim / V-brakes).
For doing the nuts up, just get an adjustable spanner, or the right sized one for the axle nuts you have and do both sides a little at a time till both sides hold where you want them. Then tighten remembering to turn the nuts the right way (it becomes second nature after a while - they're usually opposite ways to each other to tighten up !). If the wheel won't stay put then use one hand to pull it towards you as you tighten the other side.
Then adjust your brakes.
If someone has tried to tighten the axle nuts and started to screw them back on out of alignment the threads may be damaged. That's potentially more of an issue, but it's more likely the nuts got damaged than the axle !
My LBS couldn't sort my rear hub gear wheel aligment properly. I ended up doing it myself.... and replacing the washers to get the wheel to stop slipping and causing my gears to slip. 50Cycles sent me replacements for free.
Don't be put off by how hard it can seem the first couple of times. Once you do it you realize how easy it really was. It's just having to do stuff with no-one there to show you makes the learning process longer at first but in the end you'll save a load of money and time... and the (depressing) hasstle of having to keep patching and mending something you need for transport until you can get it to a shop.