Move or extend? Looking for advice

[RhubarbCrumble1]

This is a long I apologise. I'm looking for any suggestions, experience or advice.
We need more space our third tiny bedroom is my husbands office and we would like another child at some point soon.
Option one is to move at end of 5 year fixed term which is 2 years
Benefit being we can find somewhere bit bigger and with nicer nearer schools for when time comes with private garden.
Down side is the expense and hassle of moving where we'd lose money we've paid in & taking on a bigger mortgage
Option two is to knock down conservatory 2.8 metre and rebuild brick extension off kitchen
Benefit being we get a more useable room
Downside would be cost, not actually gaining more useable space and not sure an office in open would work
Option three is to take back half of garage and turn into room
Benefit this would be cheapest and less disruptive option
Downside honestly can't work out where we'd put internal access door to make it integrated into house. Kitchen has oven and cupboards against it so couldn't go through that wall. Hallway access would lead to the storage bit. Could we make smaller door leading to garage Under the stairs?
Any suggestions?
I've tried to attach pics

Advice from dh an architect:

1. Replace conservatory- you may be able to do this as a permitted development which may not require planning permission. Look at the planning portal (google it) for further information.
2. Budget around £1500/sq m for a single storey extension. It may be more or less.
3. It may be odd having an 'extra room' off the dining room. This might make a better study than a bedroom.
4. The garage - probably your best option if you can get it to work. You may be able to get the door or a link in front of the staircase. Could go further back if you have enough headroom. I'd suggest a min of 1.7m at its smallest point if a slope-y door.
5. You can add roof lights as well as the options of Windows at the back and front.
6. Replacing the garage door with a window is usually considered a permitted development as long as it's not a bay. And this won't require planning permission.
7. You may be able to reinstall your existing kitchen units on the other side to get a better door through.

Hope this helps!

How big is the 3rd bedroom at present ?

Could you build above the garage ? Take down part of the the gable wall and make bedroom 3 a more spacious bedroom, possibly with en-suite and have a study/single bedroom 4 at the front of the extension ?

Thank you so much NK5. I think we have just 1.7m under at lowest slope so good to know I'll not be laughed at if we asked.
The suggestion about cupboards being moved might work as they are only wickes one that they still have I stock
Right off to stare at walls and doors

I'd love that idea 8miss but tbh I don't love the house (area) enough to spend such a massive amount of money on it. Neither of us are handy so would need to pay someone to do it

Honestly it sounds like you'd be better off moving if poss. Course it always involves expense and hassle, but gotta be worth investigating as the current house isn't big enough, isn't great for schools and neither of you love it. If that's impossible, I'd probably make the garage into an office. The tiny bedroom won't be as much of a problem as you think for a good while yet. Many 3-beds have a small boxroom as the third bed - my DS2 (age 5) is in one now and he just uses it to sleep in. Can't see him needing more space for a good couple of years.

Honestly? I'd move. Good schools were the priority when we bought our house. Yes it's hassle at the time but worth it in the long run if you end up getting a garden and the dc I to better schools.

We just extended too, bought a run down house in a great area. Now we have a great house and area to match. Could you afford to do this?

Pink delight and Jeffrey after discussing it last night we've decided to get a quote for a small room conversion in garage for office with no internal access (access via door on back of house) and a window to keep as cheap as possible and move in 2 years when we wont get penalised for changing mortgage and the baby won't mind having a box room for a while. Really appreciate the replies

(Worlds longest sentence!)