I don't see that there is a problem with different capacity cells in parallel. It is quite common to have a lithium battery in parallel with a tantalum capacitor or two and probably a few dozen ceramic capacitors. I realise that the capacity of the lithium battery is several orders of magnitude larger than that of the capacitors, but they are all charge storage devices, and they are paralleled, and there is no problem.
Any control circuit for Li-Ion batteries will limit the charging current. With batteries in parallel, the current will be distributed between the batteries. In theory there could be a problem in that if you were charging a small cell and a large cell in parallel, the total charge current could be too large for the small battery. In practice, the charge rates are normally quite low and limited by the heating of the cell phone or its charger, not the battery. Also the charge current will tend to balance according to the battery capacities, because the voltages have to be the same.
Charging should only be done if the batteries are between 5°C and 40°C. There is only one temperature sensor for several cells in the arrangement that Akikhia suggests, so one cell could be hotter. However, in laptop batteries, there are often 3 cell in parallel, and several inches separates them, so the temperature imbalance is likely to be larger than the temperature imbalance between two flat cells that are one on top of another.
Charging must not be above 4.2 V for Li-Ion. That rule is stuck to perfectly with two cells in parallel.
Charging should be terminated when the current drops to 0.05 C. If you increase the capacity of any Li-Ion cell, then the charger should be adjusted. A charger for a 1 Ah cell will stop at 50 mA. If you charge two 1 Ah cells in parallel, the charging should stop at 100 mA for the pair. However with a 1 Ah charger, the charging will stop at 50 mA for the pair, so it will go on longer. In practice, as long as 4.2 V isn't exceeded, it won't cause a problem. The current will drop quite fast so it won't take many minutes to drop from 100 mA to 50 mA. Also, most charging circuits will restart the charging as soon as the voltage drops to 4.1 V or so. That is not significantly different from holding the cells at 4.2 V, so I can't see there being a problem there.
In all, I can't see a problem with cells in parallel.