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Just to agree with scottishpoet's responses. Your mother's ticket is OK if she makes it and you do not. But it's another reason for going via the bus transfer since if you fail conformance the Connections desk there may be (slightly) more charitable if it was due to AA being horribly late, and for example just charge the change fee on the original ticket. Obviously you can't take that for granted, and you may indeed be charged the walk up fare for the outbound and lose any return sector altogether (which doesn't apply here), at the other extreme. Cancelling the return sector is now open to legal challenge (see the CRA thread in the Dashboard).
In the circumstances it is probably best to agree to meet somewhere airside in T5 (e.g. Pilots, Itsu). If you get AA's wifi on the way back you can perhaps change that to landside once you've done the calculations and worked out that you are on time or early in terms of arrival, and thereby agree to meet landside (e.g. Carluccio). In which case, assuming you are HBO, you best go on the transfer bus and exit the UK Border there.