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If you are at the stage of thinking swapping title deeds will effect a change of ownership then you need advice (which you should pay for) and not go to the internet
There are tax implications to all this and if you do it wrong you may get a tax bill, that you can't undo by unswapping.
First of all yo need to move into each others houses and then plan the legal transfer. This will avoid something called reservation of benefit which kicks in if she trasnfers her house into your name and stays in it for any length of time.
Then legally transfer the houses (dont do this yourself)
You are now in the position ofyour mother has given you a house for no value at all. Certainly not market value. She now as to live for seven years to effect a tax free transfer on her death. Otherwise it is 40% after the first 320 000 of value.
I think
Basically you need to see a solicitor who has a tax accountant in tow or can give advice on these lines.
What is the position if she has to go into care in 18 mo. Hmmm dnt know that one.